MFA annual conference provides a forum for the interaction of finance academics and practitioners to share scholarly activity and current practice so as to encourage and facilitate the betterment of the profession. Below I select several papers with download links that are of interest to me, it is by no means a list of top quality of the conference though.

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Tags - conference

An adequate risk-adjusted return performance measure to select investment funds is crucial for financial analysts and investors. Sharpe ratio has become a standard measure by adjusting the return of a fund by its standard deviation (Sharpe, 1966), nevertheless, practitioners often question this measure mainly for its invalidity if the distribution of fund returns is beyond normal (Kao, 2002; Amin and Kat, 2003; Gregoriou and Gueyie, 2003, Cavenaile, et al, 2011, Di Cesare, et al, 2014). Several new measures have been proposed and investigated to overcome this limitation of the Sharpe ratio, however, Eling (2008)

finds choosing a performance measure is not critical to mutual fund evaluation, Eling and Schuhmacher (2007) compare the Sharpe ratio with 12 other measures for hedge funds and conclude that the Sharpe ratio and other measures generate virtually identical rank ordering, despite the significant deviations from normal distribution. Similar evaluation includes Eling and Faust (2010) on funds in emerging markets, Auer and Schuhmacher (2013) on hedge funds, and Auer (2015) on commodity investments.

This paper proves that several widely used performance measures are monotonic if the distribution of asset returns is a LS family, a family of univariate probability distributions parametrized by a location and a non-negative scale parameters that is commonly applied in finance (Levy and Duchin, 2004). Our proof certifies the empirical findings in other studies on the indifference of choosing a performance measure when valuing a fund. We show that those measures generate virtually the same rank ordering using monthly mutual fund return data from 1997 to 2005 and Monte-Carlo simulations. Therefore this paper contributes to both the academia and industry by clarifying the phenomenon.

For example, the below figure plots the correlation and confidence intervals based on 2000 simulations for each sample size. For simplicity, we show the results for the Sharpe (ρ1), the Sharpe-Omega (ρ2) and the Sortino ratio (ρ3) only. Consistent with the previous finding, the rank correlation among these performance measures is roughly equal, and is approaching one with the increase of sample size.

Tags - sharpe-ratio , mutual-fund , performance

Quotation

In this Part 1, first, we look at the tail of an asset return distribution and compress our knowledge on Value-at-Risk (VaR) to extract the essence required to understand why VaR-stuff is not the best card in our deck. Next, we move to a classical Bayes’ theorem which helps us to derive a conditional probability of a rare event given… yep, another event that (hypothetically) will take place. Eventually, in Part 2, we will hit the bull between its eyes with an advanced concept taken from the Bayesian approach to statistics and map, in real-time, for any return-series its loss probabilities. Again, the probabilities, not certainties.

Read this excellent post and accompanying Pathon codes at http://www.quantatrisk.com/2015/06/14/predicting-heavy-extreme-losses-portfolio-1/

Tags - python , portfolio , var

Quotation

Both CDS and out-of-money put option can protect investors against downside risk, so they are related while not being mutually replaceable. This study provides a straightforward linkage between corporate CDS and equity option by inferring stock volatility from CDS spread and, thus, enables a direct analogy with the implied volatility from option price. I find CDS inferred volatility (CIV) and option implied volatility (OIV) are complementary, both containing some information that is not captured by the other. CIV dominates OIV in forecasting stock future realized volatility. Moreover, a trading strategy based on the CIV-OIV mean reverting spreads generates significant risk-adjusted return. These findings complement existing empirical evidence on cross-market analysis.

Click to download

Tags - cds , volatility

Quotation

In the current literature, the analytical tractability of discrete time option pricing models is guaranteed only for rather specific types of models and pricing kernels. We propose a very general and fully analytical option pricing framework, encompassing a wide class of discrete time models featuring multiple-component structure in both volatility and leverage, and a flexible pricing kernel with multiple risk premia. Although the proposed framework is general enough to include either GARCH-type volatility, Realized Volatility or a combination of the two, in this paper we focus on realized volatility option pricing models by extending the Heterogeneous Autoregressive Gamma (HARG) model of Corsi et al. (2012) to incorporate heterogeneous leverage structures with multiple components, while preserving closed-form solutions for option prices. Applying our analytically tractable asymmetric HARG model to a large sample of S&P 500 index options, we demonstrate its superior ability to price out-of-the-money options compared to existing benchmarks.

http://www.sciencedirect.com/science/article/pii/S0304407615000615

Quotation

Volatility clustering, long-range dependence, and non-Gaussian scaling are stylized facts of financial assets dynamics. They are ignored in the Black & Scholes framework, but have a relevant impact on the pricing of options written on financial assets. Using a recent model for market dynamics which adequately captures the above stylized facts, we derive closed form equations for option pricing, obtaining the Black & Scholes as a special case. By applying our pricing equations to a major equity index option dataset, we show that inclusion of stylized features in financial modeling moves derivative prices about 30% closer to the market values without the need of calibrating models parameters on available derivative prices.

http://www.sciencedirect.com/science/article/pii/S0304407615000585

Quotation

We analyze the high-frequency dynamics of S&P 500 equity-index option prices by constructing an assortment of implied volatility measures. This allows us to infer the underlying fine structure behind the innovations in the latent state variables driving the evolution of the volatility surface. In particular, we focus attention on implied volatilities covering a wide range of moneyness (strike/underlying stock price), which load differentially on the different latent state variables. We conduct a similar analysis for high-frequency observations on the VIX volatility index as well as on futures written on it. We find that the innovations over small time scales in the risk-neutral intensity of the negative jumps in the S&P 500 index, which is the dominant component of the short-maturity out-of-the-money put implied volatility dynamics, are best described via non-Gaussian shocks, i.e., jumps. On the other hand, the innovations over small time scales of the diffusive volatility, which is the dominant component in the short-maturity at-the-money option implied volatility dynamics, are best modeled as Gaussian with occasional jumps.

http://www.sciencedirect.com/science/article/pii/S0304407615000627

Quotation

The paper proposes a general asymmetric multifactor Wishart stochastic volatility (AMWSV) diffusion process which accommodates leverage, feedback effects and multifactor for the covariance process. The paper gives the closed-form solution for the conditional and unconditional Laplace transform of the AMWSV models. The paper also suggests estimating the AMWSV model by the generalized method of moments using information not only of stock prices but also of realized volatilities and co-volatilities. The empirical results for the bivariate data of the NASDAQ 100 and S&P 500 indices show that the general AMWSV model is preferred among several nested models.

http://www.sciencedirect.com/science/article/pii/S0304407615000548

Quotation

We introduce a tractable class of multi-factor price processes with regime-switching stochastic volatility and jumps, which flexibly adapt to changing market conditions and permit fast option pricing. A small set of structural parameters, whose dimension is invariant to the number of factors, fully specifies the joint dynamics of the underlying asset and options implied volatility surface. We develop a novel particle filter for efficiently extracting the latent state from joint S&P 500 returns and options data. The model outperforms standard benchmarks in- and out-of-sample, and remains robust even in the wake of seemingly large discontinuities such as the recent financial crisis.

http://www.sciencedirect.com/science/article/pii/S0304407615000597

Quotation

Assume that St is a stock price process and Bt is a bond price process with a constant continuously compounded risk-free interest rate, where both are defined on an appropriate probability space P. Let yt=log(St/St−1). yt can be generally decomposed into a conditional mean plus a noise with volatility components, but the discounted St is not a martingale under P. Under a general framework, we obtain a risk-neutralized measure Q under which the discounted St is a martingale in this paper. Using this measure, we show how to derive the risk neutralized price for the derivatives. Special examples, such as NGARCH, EGARCH and GJR pricing models, are given. Simulation study reveals that these pricing models can capture the “volatility skew” of implied volatilities in the European option. A small application highlights the importance of our model-based pricing procedure.

http://www.sciencedirect.com/science/article/pii/S030440761500055X

Tags - option

Quotation

Using the Chinese stock market data from 1997 to 2013, this paper examines the “Sell in May and Go Away” puzzle first identified by Bouman and Jacobsen (2002). We find strong existence of the Sell in May effect, robust to different regression assumptions, industries, and after controlling for the January or February effect. However, part of the puzzle is subsumed by the seasonal affective disorder effect. We then construct a trading strategy based on this puzzle, and find that it outperforms the buy-and-hold strategy and could resist the market downside risk during large recession periods.

As the abstract suggests, basically we aim to examine whether the sell-in-may phenomenon existed in developed country also happens in China, and if Yes, if there is any special reason to explain it, which has implications for those international investors as MSCI plans to add Chinese A shares to its emerging index from May 2015, and as the recent China's stock market plan that permits Hong Kong investors to trade designated stocks in Shanghai Exchange market directly. People would expect investing in China provides a diversified strategy.

“Sell in May and Go Away” puzzle means that stocks have higher returns in the November-April period than the May-October period, in this paper we first run a dummy regression that assign dummy=0 when the date t is in the May-October period, and dummy=1 when otherwise. We find the dummy variable is highly significant, not driven by a specific industry, and cannot be explained by well-known January or February effect, nor by time-varying risk, nevertheless, time-varying risk aversion approximated by the SAD (seasonal affective disorder) effect by Kamstra, et al. (2003) subsumes part of the Sell in May effect.

Then we test whether such a phenomenon could generate any economic benefit, We construct a trading strategy that buys the Chinese stock market at the beginning of November and sells it at the end of April of the next year. We save the capital in a bank earning a risk-free floating deposit rate from the beginning of May to the end of October . Our benchmark is a buy-and-hold strategy. This simple trading strategy is shown to outperform the buy-and-hold strategy and can protect investors from dramatic losses during large recession, as shown in belowing Table and Figure.

Sell in May strategy Buy-and-hold strategy

Return 13.03% 7.50%

Sharpe ratio 0.6002 0.2199

Maximum drawdown 27.00% 69.30%

Downside deviation 2.98% 5.34%

Historical VaR (95%) 6.86% 11.20%

Leland’s alpha 8.69%

The short paper is at http://www.sciencedirect.com/science/article/pii/S1544612314000579

Quotation

In this paper, we propose a trend factor to capture cross-section stock price trends. In contrast to the popular momentum factor constructed by sorting stocks based on a single criterion of past year performance, we form our trend factor with a cross-section regression approach that makes use of multiple trend indicators containing daily, weekly, monthly and yearly information. We find that the average return on the trend factor is 1.61% per month, more than twice of the momentum factor. The Sharpe ratio is more than twice too. Moreover, during the recent financial crisis, the trend factor earns 1.65% per month while the momentum factor loses 1.33% per month. The trend factor return is robust to a variety of control variables including size, prior month return, book-to-market, idiosyncratic volatility, liquidity, etc., and is greater under greater information uncertainty. In addition, the trend factor explains well the cross-section decile portfolio returns sorted by short-term reversal, momentum, and long-term reversal as well as various price ratios (e.g. E/P), and performs much better than the momentum factor.

The basic idea is to first calculate the month-end price moving average time series of different lags, then regress cross-sectionally monthly returns at date t on all moving average series at date t-1, finally predict monthly returns at date t+1 using the regression estimates and the moving average series at date t. This procedure guarantees we forecast stock returns at t+1 with information set only up to t. We then rank all stocks based on the forecasts into five quintiles, long the quintile with highest forecast returns and short the quintile with lowest, and rebalance once per month. This strategy generates, on average, 1.61% monthly return and 0.29 sharpe ratio using all US stocks, performs especially good during recession, and outperforms several existing factors. Moreover, the good performance of this strategy cannot be explained by firm fundamentals.

I implement this strategy with Chinese stock data, adjust the rebalance frequency to weekly for convenience, and trade in extreme by always long the one stock with the highest forecast return, no short is allowed, stop loss is set at 5%. The result is amazing, it yields an annualized return at 97.15% from March, 2013 to Feb, 2014, with maximum drawdown at 30.01%. The fund curve is as follows (note: I didn't use all Chinese stocks but only 840 stocks in my stock pool with good liquidity, so there is selection bias and please accept the result cautiously...)

Nice shot. It seems to be better than the simple strategy between A-shares and H-shares.

Tags - trend , strategy , china

At the moment there are 84 firms listed at both A (Shanghai and Shenzhen) and H (Hongkong) stock markets, according to the law of one price, the stock prices of these firms should be at similar level. However, there are huge differences, without considering exchange rate (1 RMB = 1.28 HK$), the ratio of the price in A market to the price in H market for a same firm is as low as 52.72% and as high as 617.59% as of 02/03/2014. Is the difference mean reverting? If yes, we would expect the stock traded cheaper in A market to go up, and vice versa. So can we make profit by long the stocks with large differences?

Rigorous statistical method should be undertaken to examine whether the ratio is indeed mean reverting. For simplicity, I construct a trading strategy that each week, I go long at the opening price the stock in A market that has the smallest price ratio of previous week, hold it one week and sell it at the weekly closing price. Short trading is not allowed for individual investor in A market. Stop loss is set arbitrarily at 5%. Transaction cost is 0.18% per trading.

The results for this simple strategy from 02.2013 to 01.2014 are:

Annualized Return 0.2070

Annualized Std Dev 0.2545

Annualized Sharpe 0.8133

Maximum Drawdown

From Trough To Depth Length To Trough Recovery

1 2013-09-13 2013-12-13 -0.1275 19 12 NA

2 2013-08-16 2013-08-23 2013-09-06 -0.0566 4 2 2

3 2013-03-22 2013-04-19 2013-05-03 -0.0488 5 3 2

4 2013-07-12 2013-07-12 2013-07-19 -0.0374 2 1 1

5 2013-05-31 2013-05-31 2013-07-05 -0.0229 6 1 5

The fund curve

Lower line is the return for a buy-and-hold strategy of all 84 firms.

Considering the fact that 2013 is a gloomy year for A market and this strategy is long only, the performance is not bad at all. Comments are welcomed

Tags - strategy , china

Thinknum is a web platform that enables investors to collaborate on financial analysis, it aggregates the abundance of financial data and insights on the web and presents it to our users in an intuitive format, indexing the world’s financial information in the process.

Thinknum’s Cashflow Model allows users to value companies based on fundamentals just like Wall Street research analysts do. All the assumptions that go into the valuation models are visible and editable. The data for the models is also updated automatically when companies publish their quarterly filings.

The Plotter allows users to track financial data, analyze trends, and perform expressions such as regressions and correlations without having to write code. Thinknum currently provides data from over 2,000 sources.

A few experts have written about Thinknum:

• Jason Voss of the CFA Institute published a comprehensive overview of Thinknum’s mission.

• Francis Smart discussed Thinknum’s integration with R on R-Bloggers.

Thinknum was founded in 2013 by Gregory Ugwi and Justin Zhen, two friends who met at Princeton University in 2006. After graduation, Gregory went to work for Goldman Sachs and Justin worked at a hedge fund, where they both discovered the major flaws with existing financial data analysis tools. That’s when they decided to create a superior platform for all types of investors.

Thinknum is constantly adding new features, so join their community and sign up for free today at thinknum.com.

Tags - site

Bloomberg Businessweek, commonly and formerly known as BusinessWeek, is a weekly business magazine published by Bloomberg L.P. Founded in 1929, the magazine was created to provide information and interpretation about what was happening in the business world. BusinessWeek was first published in September 1929, only weeks before the stock market crash of 1929. The magazine provided information and opinions on what was happening in the business world at the time. Early sections of the magazine included marketing, labor, finance, management and Washington Outlook, which made BusinessWeek one of the first publications to cover national political issues that directly impacted the business world.

I am offered a 15% off coupon for Bloomberg Businessweek, so should you are interested, you can order 16 Issues of Bloomberg Businessweek for $15! (That's an 81% Savings)!.

Tags - coupon

Quotation

We propose a new definition of skill as a general cognitive ability to either pick stocks or time the market at different times. We find evidence for stock picking in booms and for market timing in recessions. Moreover, the same fund managers that pick stocks well in expansions also time the market well in recessions. These fund managers significantly outperform other funds and passive benchmarks. Our results suggest a new measure of managerial ability that gives more weight to a fund’s market timing in recessions and to a fund’s stock picking in booms. The measure displays far more persistence than either market timing or stock picking alone and can predict fund performance.

Paper.

Tags - mutual-fund , skill

This package calculates the European put and call option prices using the Corrado and Su (1996) model. This method explicitly allows for excess skewness and kurtosis in an expanded Black-Scholes option pricing formula. The approach adapts a Gram-Charlier series expansions of the standard normal density function to yield an option price formula that is the sum of a Black–Scholes option price plus adjustment terms for nonnormal skewness and kurtosis (Corrado and Su, 1997).

For skewness = 0 and kurtosis = 3, the Corrado-Su option prices are equal to the prices obtained using the Black and Scholes (1973) model.

You can download the Matlab code at Corrado and Su (1996) European Option Prices.

References:

Corrado, C.J., and Su T. Skewness and kurtosis in S&P 500 Index returns implied by option prices. Financial Research 19:175–92, 1996.

Corrado, C.J., and Su T. Implied volatility skews and stock return skewness and kurtosis implied by stock option prices. European Journal of Finance 3:73–85, 1997.

Hull, J.C., "Options, Futures, and Other Derivatives", Prentice Hall, 5th edition, 2003.

Luenberger, D.G., "Investment Science", Oxford Press, 1998.

Tags - black scholes , skewness , kurtosis , option

Quotation

We propose a model of portfolio selection that adjusts an investors’ portfolio allocation in accordance with changing market liquidity environments and market conditions. We found that market liquidity provides a useful “leading indicator” in dynamic asset allocation. Specifically, market liquidity risk premium cycles anticipate economic and market cycles. Investors can therefore act to avoid markets with low liquidity premiums, waiting to extract liquidity risk premiums when the likelihood of extracting a liquidity premium improves. The result, meaningfully enhanced portfolio performance through economic and market cycles, and is robust to transactions costs and alternate specifications.

Basically this article examines a portfolio strategy that buys stocks and sells bonds when the market is less liquid, thus enjoying a higher liquidity premium, this strategy outperforms a benchmark with equal weights on stocks and bonds by generating a higher sharpe ratio and positive alpha.

Journal paper Working paper

Tags - liquidity , portfolio , allocation

Quotation

We propose that fund performance can be predicted by its R2, obtained from a regression of its returns on a multifactor benchmark model. Lower R2 indicates greater selectivity, and it significantly predicts better performance. Stock funds sorted into lowest-quintile lagged R2 and highest-quintile lagged alpha produce significant annual alpha of 3.8%. Across funds, R2 is positively associated with fund size and negatively associated with its expenses and manager's tenure.

Journal paper, Working paper.

Tags - mutual-fund , prediction

Quotation

Since Lehman Brothers collapsed in 2008, tail-risk hedging has become an increasingly important concern for investors. Traditional approaches, such as purchasing options or variance swaps as insurance, are often expensive, illiquid, and result in a substantial drag on performance. A more prudent, cost-effective way to maintain a constant risk exposure is to actively manage portfolio exposure according to the prevailing volatility level within underlying assets. The authors implement a robust methodology based on Dybvig’s payoff distribution model to target a constant level of volatility and normalize monthly returns. This approach to portfolio and risk management can help investors obtain their desired risk exposures over both short and longer time frames, reduce exposure to tail risk, and in general increase portfolios’ risk-adjusted performance.

The idea is simple, easy to implement, has a good performance based on the authors' results.

Journal paper, Working paper.

Tags - volatility , tail , risk , portfolio

Quotation

Portfolio optimization problems involving value at risk (VaR) are often computationally intractable and require complete information about the return distribution of the portfolio constituents, which is rarely available in practice. These difficulties are compounded when the portfolio contains derivatives. We develop two tractable conservative approximations for the VaR of a derivative portfolio by evaluating the worst-case VaR over all return distributions of the derivative underliers with given first- and second-order moments. The derivative returns are modelled as convex piecewise linear or—by using a delta–gamma approximation—as (possibly nonconvex) quadratic functions of the returns of the derivative underliers. These models lead to new worst-case polyhedral VaR (WPVaR) and worst-case quadratic VaR (WQVaR) approximations, respectively. WPVaR serves as a VaR approximation for portfolios containing long positions in European options expiring at the end of the investment horizon, whereas WQVaR is suitable for portfolios containing long and/or short positions in European and/or exotic options expiring beyond the investment horizon. We prove that—unlike VaR that may discourage diversification—WPVaR and WQVaR are in fact coherent risk measures. We also reveal connections to robust portfolio optimization.

Journal, Working paper in PDF.

Tags - var , nonlinear , risk

Below are three sets of frequently asked questions (FAQs) that relate to counterparty credit risk, including the default counterparty credit risk charge, the credit valuation adjustment (CVA) capital charge and asset value correlations. More sets may be forthcoming, stay tuned.

First set

Second set

Third set

Fourth set

Tags - basel , faq , counterparty , credit

"How to Combine Long and Short Return Histories Efficiently" is a good paper forthcoming in Financial Analysts Journal by Sébastien Page, as introduced

Quotation

A common challenge in portfolio risk analysis is that certain assets have shorter return histories than others. Unfortunately, many standard portfolio risk analysis techniques—including historical tail risk measurement, regime-dependent risk analysis, and bootstrapping simulations—require full return histories for all assets or risk factors. The author presents easy instructions on how to efficiently combine data for investments whose histories differ in length and offers a new model to better account for non-normal distributions.

An important feature of this paper is instead of assuming that the uncertainty around the backfilled returns is normally distributed, the model samples empirical residuals from the short sample. Evidence shows this method is efficient. The author also provides Matlab code in the Appendix for us to play around.

Paper

Tags - missing , imputation , mle , em , distribution

Whether it is the risk of falling behind, peer group pressure or ill-defined incentive schemes, there exists a tendency to choose direction based on the illusion of control when there is actually too much uncertainty. Instead, questions should be asked as to whether decisions based on more or less unfounded assumptions should be made at all. Unfounded and inappropriate assumptions are dangerous because of at least two well-known biases. First, we tend to be over-confident in our ability to make financial and economic probability models. The second bias is our tendency to favour information that confirms our beliefs or hypotheses. This is called the confirmation bias. Moreover, by using hyperbolic discounting we reveal a strong tendency to make choices that are inconsistent over time. In other words, we make choices today that our future self would prefer not to make, despite using the same reasoning. Therefore, CRO’s and all other professionals should minimize their bold assumptions about how the economy works. We know much less than we think we know. Warren Buffet, the highly successful investor, sets strict restraints on using assumptions. He nevertheless makes above average profits.

The volatility is wrong when you really need it. When reading this sentence most risk managers immediately think about skewness, kurtosis or perhaps about extreme losses. However, it is necessary to take it one step further. Most of the risk indicators, also in a regulatory context, are based on statistics. In most circumstances this is a second moment, named "variance" or "volatility". The volatility is however an affect heuristic driven indicator. It has no real correlation with the actual risk. The affect heuristic leads people to have a low perception of risk when we feel positive about the economy (and the other way around). However, during long periods of bull markets – driven by debt accumulation – actual risk (e.g. the probability of a deep debt crisis) increases, but our perception of risk reduces.

What you are really interested in is the consequence of market shocks when it actually goes terribly wrong. In this way you correlate risk with the probability of survival of your firm. The use of volatility is a good example of attribute substitution. A complex problem (what are the consequences of a serious meltdown) is replaced with a less complex problem (what is the observed volatility of the market over the last few months/years), at which point the answer to the less complex problem is seen as the solution to the original problem. Risk indicators should be correlated with actual risk, not with indicators such as (implied) volatility. A better risk indicator is the price to profit ratio of stocks, which reveals – in combination with debt levels – a lot about instability accumulating in an economy.

There is a combination of eagerness to use complex models and too high a dependence on (recent) data that makes the use of models tricky at the very least. The quantitative models used in the financial sector are not fit for their purpose. For the models to perform reasonably well they need more regime shifts and more chaos components. For example, when we add debt to macro-economic models, they become very unstable. The economy and the financial markets follow an almost chaotic process. This, however, makes models almost impossible to calibrate. Additions, such as jump diffusion, copulas and stochastic volatilities are well-intentioned attempts to bring the models closer to reality, but this is still not close enough. We know reality is much more unstable. But, we don't like ambiguity, so we replace this with clear models. However, in the end they are still based on the implausible assumption of a stable repeating data generating process. Complex models also challenge our biased cognitive abilities. This especially holds true for the interpretation of model results. It is better to use simple models and perform many back- and stress tests and to focus on the underlying data, including data from past debt crises.

According to Shiller, the human mind thinks in terms of stories, with internal logic and dynamics that appear as a unified whole. Taleb calls it "explanations (stories) bind facts together". There is a direct link between the content of stories, the collective confidence and the booms and busts of the financial markets. The spread of stories, and thus the collective confidence or pessimism, could be compared to an epidemic, which tends to spread extremely quickly and without warning. This is why the economy follows an almost chaotic process. Collective confidence does not necessary mean a strong economy; even worse, it can lead to growing instability. One should remember that it does not matter what something looks like, it's how it behaves that counts. What makes it even more confusing is that the models seem to prove the story. The estimations based on data seem to be statistically significant, but in reality this is false. The underlying process changes when an economy tips! The CRO should not blindly follow the herd. Thinking in advance about other stories will improve the chance of survival when the stories start to change. Directly related to this topic is the use of scenario thinking in risk management. With proper scenarios, which are at the very heart of risk management – the minimization of unbearable loss – will be more successful.

As we have already seen, the brain makes decisions based on simplifications or so-called rules of thumb. These heuristics and biases have a tendency to deviate our decision-making from rationality and are at the root of our structurally making the same mistakes over and over again. Even if models work correctly, the resulting decision can still be irrational, usually because of (unconscious) emotions. Emotions and behaviour play a large role in decision-making. Seemingly rational decisions are actually driven by fear, loss aversion and affective forecasting. For example, people act completely differently when they are confronted with a loss than when they find themselves in a profit situation. This is a well-known and important aspect of Prospect Theory that is known as "aversion to a sure loss". Many more of these emotional aspects, that make us decide depending on the emotional state we're in, are known. Understanding all of this, it seems strange that no one in financial institutions is formally given the role of monitoring the behaviour and emotions of the senior management. Perhaps supervisory boards should consider hiring behavioural specialists. At the very least, the senior management and thus the CRO, should start conducting behavioural self-assessments.

Tags - quant , magazine

I would like to express utmost thanks to my supervisor, Professor David Newton, for his continued encouragement, support and guidance throughout the course of my PhD research. I am grateful for his patience, interest and willingness to accept my PhD research topics. Not only does he provide me with research guidance but also his advice for my career drives the whole course of research and makes the three-year PhD study in Nottingham much more interesting.

I thank my parents for their unconditional love and understanding. My life wouldn’t be as it is now without their selfless support. I also want to thank Ms. Haoyu Ma, who has always been at my side supporting me throughout this whole research. Your love and support make every mission possible.

I also take this opportunity to show my thanks to my PhD colleagues and friends at the Nottingham University Business School for their encouragement and help. Spending three fantastic years with you is memorable for the rest of my life. In particular, I would like to thank Dr. Huainan Zhao, Dr. Kai Dai, Ms. Ting Qiu and Mr. Ding Chen, who have always provided me with invaluable advice and suggestions, and helped me in the many ways they can.

Importantly, I thank my co-authors, Dr. Qian Han, Dr. Doojin Ryu, Dr. SongTao Wang, and Prof. David Newton. Our publications and working papers would not be so great without your collaboration. I also appreciate the fly-out opportunities given by University of Otago (New Zealand), Renmin University (China), and KAIST (Korea Advanced Institute of Science and Technology), I had very good time and the experience is memorable no matter an offer will be given or not.

Finally, thanks for your continue reading my blog despite my infrequent posts this year. A photo taken few weeks ago when I visit a famous temple in HangZhou, China, wish you all healthy and successful in the coming year.

Tags - thanksgiving

Below are three sets of frequently asked questions (FAQs) that relate to counterparty credit risk, including the default counterparty credit risk charge, the credit valuation adjustment (CVA) capital charge and asset value correlations. More sets may be forthcoming, stay tuned.

First set

Second set

Third set

Tags - risk , counterparty , basel , credit , cva

Basically RunMyCode is a novel cloud-based platform that enables scientists to openly share the code and data that underlie their research publications. It has many files accompanying those published papers so you can easily replicate the results, which dramatically decreases your research efforts. You can choose to download the coding files directly, or upload your data and run it via the site's cloud platform. (I tried twice but failed for unknown reasons, so I recommend you to download the file and run on your own computer.)

The site is a newly established and is expanding, at the moment it includes 64 files under the following categories

A sample search in Finance returns you the codes.

It is free to use, quite nice, isn't it?

Tags - code

Quotation

Going beyond the simple bid–ask spread overlay for a particular Value at Risk, the author introduces an innovative framework that integrates liquidity risk, funding risk, and market risk. He overlaid a whole distribution of liquidity uncertainty on future market risk scenarios and allowed the liquidity uncertainty to vary from one scenario to another, depending on the liquidation or funding policy implemented. The result is one easy-to-interpret, easy-to-implement formula for the total liquidity-plus-market-risk profit and loss distribution.

Journal paper, Working paper

Tags - liquidity , var , risk

Quotation

This paper proposes a framework for the modeling, inference and forecasting of volatility in the presence of level shifts of unknown timing, magnitude and frequency. First, we consider a stochastic volatility model comprising both a level shift and a short-memory component, with the former modeled as a compound binomial process and the latter as an AR(1). Next, we adopt a Bayesian approach for inference and develop algorithms to obtain posterior distributions of the parameters and the two latent components. Then, we apply the model to daily S&P 500 and NASDAQ returns over the period 1980.1–2010.12. The results show that although the occurrence of a level shift is rare, about once every two years, this component clearly contributes most to the variation in the volatility. The half-life of a typical shock from the AR(1) component is short, on average between 9 and 15 days. Interestingly, isolating the level shift component from the overall volatility reveals a stronger relationship between volatility and business cycle movements. Although the paper focuses on daily index returns, the methods developed can potentially be used to study the low frequency variation in realized volatility or the volatility of other financial or macroeconomic variables.

Journal paper, Working paper in PDF

Tags - stochastic , volatility

Quotation

We test the performance of different volatility estimators that have recently been proposed in the literature and have been designed to deal with problems arising when ultra high-frequency data are employed: microstructure noise and price discontinuities. Our goal is to provide an extensive simulation analysis for different levels of noise and frequency of jumps to compare the performance of the proposed volatility estimators. We conclude that the maximum likelihood estimator filter (MLE-F), a two-step parametric volatility estimator proposed by Cartea and Karyampas (2011a; The relationship between the volatility returns and the number of jumps in financial markets, SSRN eLibrary, Working Paper Series, SSRN), outperforms most of the well-known high-frequency volatility estimators when different assumptions about the path properties of stock dynamics are used.

Journal paper, Working paper

Tags - volatility

A paper "

Quotation

This paper proposes a simple model for incorporating wrong-way and right-way risk into CVA (credit value adjustment) calculations. These are the calculations, involving Monte Carlo simulation, made by a dealer to determine the reduction in the value of its derivatives portfolio because of the possibility of a counterparty default. The model assumes a relationship between the hazard rate of the counterparty and variables whose values can be generated as part of the Monte Carlo simulation. Numerical results for portfolios of 25 instruments dependent on five underlying market variables are presented. The paper finds that wrong-way and right-way risk have a significant effect on the Greek letters of CVA as well as on CVA itself. It also finds that the percentage effect depends on the collateral arrangements.

Article, Working paper.

Tags - cva , default , credit , crisis , portfolio

An excellent review book on liquidity and asset prices by three experts Yakov Amihud, Haim Mendelson, and Lasse Heje Pedersen. A good bed reading one.

Quotation

We review the theories on how liquidity aﬀects the required returns of capital assets and the empirical studies that test these theories. The theory predicts that both the level of liquidity and liquidity risk are priced, and empirical studies ﬁnd the eﬀects of liquidity on asset prices to be statistically signiﬁcant and economically important, controlling for traditional risk measures and asset characteristics. Liquidity-based asset pricing empirically helps explain (1) the cross-section of stock returns, (2) how a reduction in stock liquidity result in a reduction in stock prices and an increase in expected stock returns, (3) the yield differential between on- and oﬀ-the-run Treasuries, (4) the yield spreads on corporate bonds, (5) the returns on hedge funds, (6) the valuation of closed-end funds, and (7) the low price of certain hard-to-trade securities relative to more liquid counterparts with identical cash ﬂows, such as restricted stocks or illiquid derivatives. Liquidity can thus play a role in resolving a number of asset pricing puzzles such as the small-ﬁrm eﬀect, the equity premium puzzle, and the risk-free rate puzzle

Download Book here.

Tags - liquidity , return

Quotation

We propose a new method for measuring the quality of banks' credit portfolios. This method makes use of information embedded in bank share prices by exploiting differences in their sensitivity to credit default swap spreads of borrowers of varying quality. The method allows us to derive a credit risk indicator (CRI). This indicator represents the perceived share of high-risk exposures in a bank's portfolio and can be used as a risk weight for computing regulatory capital requirements. We estimate CRIs for the 150 largest U.S. bank holding companies. We find that their CRIs are able to forecast bank failures and share price performances during the crisis of 2007–2009, even after controlling for a variety of traditional asset quality and general risk proxies.

Article, Working paper

Tags - crisis , cds , credit , risk , bank

Investors across the globe aspire to use the Bloomberg terminal which certainly gives a deep insight to almost everything from the world of investments. The guide which follows provides you with all possible information on the Bloomberg Terminal. The guide provides an overview of the following topics:

• Starting and Installing the terminal

• Navigating through the options

• Checking out Tickers

• Accessing the Help Options

• Sending Messages

• Getting Updates and News

• Analysis of the Securities

The Bloomberg System requires the installation of a high functioning keyboard that comes with special keys especially made for this terminal. The crucial part for a layman is that he needs to be conversant with the navigation controls that find a discussion below.

A Bloomberg Terminal can be initiated in two ways. You can contact the Bloomberg team so that the customer care executive can list down your needs and send a sales representative to contact you accordingly. It is a noteworthy fact that the terms and conditions of the contract differ with respect to the priorities of different users and therefore is different for every user. The software being expensive, it may not sound practicable to install a separate terminal for each user. Though the software is fit to be installed into certain operating systems that are more common, the company gives a specially designed and enabled keyboard.

As soon as the installation is complete, the users need to learn the navigation process which begins with the login page where the user needs to put the login requisites as provided by the company.

The Bloomberg Terminal comes with an entirely different interface as compared with the more common ones of the ordinary system. Besides containing all the keys that an ordinary keyboard contains, the special keyboard for the terminal contains two extra keys above the F1 to F12 keys. These extra keys help the user to access the advanced features which come with this software.

In order to examine a stock, you just need to press the EQUITY button. The CURRENCY button helps you to compare the rates of the US dollars with that of the EURO and also other currencies. Through the MESSAGE key you can communicate with other users or can even send your GRABS via emails into your inbox. Every other relevant information is provided about the terminal as you go to the HELP key.

The Bloomberg Terminal depends on tickers and abbreviations for all its functioning. When you want to view a specific stock such as that of the Polaris Industries Inc. you just need to type in (PII) following which you need to press the EQUITY key and then press the enter key. The screen that comes up shows all the particulars concerning the stock. As a layman, one may not know all the operations and functions associated with the terminal. A regular user can grab in the functions and shortcuts with time and experience. Some of the most used shortcuts include MSFT DES DIV CACS and others. Given the variety of functions offered by the terminal it is advisable to use the menus in which you can select the functions you require.

The Bloomberg Terminal primarily aims at analysing the individual investments. While it monitors and records the market movements, it keeps a track of the news so as to be updated with the latest information. You can make your choice from a number of options available and also can lock the specific area or field for which you need the news updates. Suppose if a person residing in the United States wants to be updated with the news of stock market e.g. NYSE or NASDAQ, Bloomberg Terminal enables him to fix his choice. With the TOP function you can also update yourself with the fresh news of the hour. You can avail of the facility of monitoring the market movement as the terminal gives you all the coverage of the market movement which provides you with the knowledge of different market sector as well as private asset classes.

The Bloomberg Terminal is built up with the special feature that enables you to monitor the economic forecasts as well as other releases. By typing in ECO GO the user can have access to the main economic page where every data concerning economics is present. The user can be aware of the current state of economics, the current economic forecasts and the data releases. You can even make yourself acquainted with the views of all the internationally famous economists. For your output, you get to see the postings on the screen displayed before you, where you also get to see the updates. The dropdown menus help you to browse in accordance with the regions you specify from the option Region. You can also specify to your terminal the country that you want to follow.

One of the foremost functions of the Bloomberg Terminal is to analyse the individual securities. The system has a great capacity and asset classes are mostly included, viz.:

• Equities

• Currencies

• Fixed Income securities

• Commodities

• ETFs

• Mutual Funds

• And a few more

If you are a layman or a beginner, you are required to follow certain basic functions while you are also provided with certain facilities. The Bloomberg team comes at your assistance in case you are troubled with any of the functions of the terminal. The foremost thing that most of the users do is searching the tickers for the particular field with which they are concerned. For example, if you hit the asset class (example, EQUITIES) and then type TK and then the security name (example, Polaris), the ticker referring to the security name is instantly displayed before you. If the stock that you have been searching is listed over numerous exchanges, you will be shown all the tickers related to the security name. It however requires mention that the name of the security should be typed with the correct spelling so as to avoid delays in displaying the results. It should also be seen that the security name should be specific.

As soon as you choose your ticker the starting page appears. This is the description page. The page can be accessed with no delay if the user knows the ticker. The user just needs to type DES “security ticker”. The description page shows such details as market capitalization, dividend yield, price quote, 52 week high/low, P/E ratio and more. The terminal even enables its users to have updates and information on the details of contact of the company concerned. It also makes the user aware of the breakup of earnings and revenue which depends on the location of the place, geographically. The user can go through the record of the financial side of the company.

The Bloomberg Terminal becomes all the more useful in case you want to retrieve the history of the price of a particular security for which you are eager to know the patterns of trading. You can do this by simply typing in HP and a screen will appear before you showing all the prices of the security. The terminal offers the advanced suite enabled with charting capacity for the users who want more advanced technical analysis. Bollinger bands, relative strength indicators, charts designed to compare different securities, and volume charts are some of the tools that are provided by the Bloomberg Terminal. Through this unique terminal you can even have access to the updates of a particular company of your interest.

This serves as a guide that comes handy for you if you choose to initiate yourself into using the Bloomberg Terminal. It provides the beginner with a guide for the basics of the terminal. For more advanced and in-depth knowledge into the software it is recommended to refer to the Bloomberg helpdesk where the concerned professionals solve all the queries. Anyone finding interest in the positions of the financial market can avail of the uses offered by the terminal. Other than its expense, Bloomberg Terminal has come up to be boon for its users. The terminal keeps the enthusiastic users updated with the news and updates of the financial market. In case if you have a query regarding the terminal or if you have trouble operating the system, you can post your query. I will answer your queries with pleasure.

Tags - bloomberg

R/Finance 2012: Applied Finance with R: slides for the R/Finance 2012: Applied Finance with R conference.

Black-Scholes Option Pricing in MATLAB using the NAG Toolbox: how to use the NAG Toolbox for MATLAB to replace some of the option pricing routines in the Finance Toolbox.

Tags - attribution , r , nag , black scholes

Quotation

We investigate a new non-stationary non-parametric volatility model, in which the conditional variance of time series is modelled as a non-parametric function of an integrated or near-integrated covariate. Importantly, the model can generate the long memory property in volatility and allow the unconditional variance of time series to be time-varying. These properties cannot be derived from most existing non-parametric or semi-parametric volatility models. We show that the kernel estimate of the model is consistent and its asymptotic distribution is mixed normal. For an empirical application of the model, we study the daily S&P 500 index return volatility using the VIX index as the covariate. It is shown that our model performs reasonably well both in within-sample and out-of-sample forecasts.

article, or working paper.

Tags - non-parametric , volatility , vix

Pat at Portfolio Probe recently had a wonderful test on some heuristic optimization methods, including simulated annealing, traditional genetic algorithm, evolutionary algorithms. By using R packages and functions - Rmalschains, GenSA, genopt, DEoptim, soma, rgenoud, GA, NMOF and SANN method of optim, he finds that the Rmalschains and GenSA packages are standing out. Nice one, original article is at A comparison of some heuristic optimization methods.

Tags - r , optimization

Regime Switching Model with constant transition probability matrix.

Click here for an introduction paper and Matlab codes are here.

Tags - markov , matlab , regime

Institute of Mathematics of the National Academy of Sciences in association with Yerevan State University and American University of Armenia is organizing a Workshop on Stochastic and PDE Methods in Financial Mathematics in September 7 - 12, 2012 to be held in Yerevan, Armenia.

The program of the workshop will consist of invited 50 minutes plenary lectures and contributed 20 minutes talks, poster sessions as well as short presentations.

The registration deadline is August 10, 2012. The deadline for abstract submission is July 31, 2012.

Online registration is available at:

http://math.sci.am/conference/sept2012/registration.html

e-mail: mathconf@gmail.com, mathconf@ysu.am

web page: http://math.sci.am/conference/sept2012/index.html

Fax: (+374 10) 524801

We are looking forward to see you in Armenia in September, 2012!

With kind regards,

Michael Poghosyan

Department of Mathematics and Mechanics

Yerevan State University,

Alex Manoogian 1, 0025, Yerevan, Armenia.

Tags - pde , stochastic , conference

Tags - forecast , portfolio , strategy , r , correlation , volatility , skew

A new

American options,

European options,

Asian options,

Barrier options,

Binary options,

Currency translated options,

Lookback options,

Multiple assets options and

Multiple exercises options

European options,

Asian options,

Barrier options,

Binary options,

Currency translated options,

Lookback options,

Multiple assets options and

Multiple exercises options

Many more models are being implemented currently and will be added soon to AirXCell. In addition to the

This form is very valuable to quantitative researchers or any finance professional who needs to compute theoretical option prices easily and who is looking for a reliable option pricer.

The Option pricing form presents the user with an HTML form enabling her to set up the model with the required parameters values such as the underlying asset price, the strike price, the volatility of the underlying asset, etc.

For instance, the following form is presented to a user requesting the price of an european option using the Generalized Black Scholes model:

Again, there are many more models and option types coming soon as well as other forms for various other kind of calculations, still mostly oriented towards financial calculation.

Tags - option , pricing , r

Tags - liquidity , risk , var , option , return , jpmorgan

Tags - return , forecast , volatility , big-data

Many people grossly mis-estimate just how much hedge fund managers make, often quoting celebrities they assumed to of earned more. The fact is that this elite group generally goes by unreported and anonymous despite the fact they make more than the GDP equivalent of many small countries combined, every year, even in the depths of one of the worse financial recessions the world has seen for decades.

Uncover the secrets of the elite group that makes up the worlds richest hedge fund managers and share with your friends in this catch infographic!

Click here for a larger pic.

Infographic by BrokerReview.org - a user driven social comparison site for online stock and forex brokers.

Tags - hedge , fund, , manager, , rich

**First International Conference on Futures and other Derivative Markets**

15-16 October 2012

Beihang University, Beijing, China

________________________________________

The Shanghai Futures Exchange, Beihang University and Renmin University of China are jointly organizing a conference on the topic of futures and other derivative markets. This conference aims to join academics and business economists to discuss a wide variety of topics on global derivative especially futures markets and their implications for practitioners.

Submission: Complete papers should be sent to DerivativeConference@gmail.com by July 8, 2012. Feel free to address any enquiries to this address as well.

Participation: There is no registration fee for the conference. Presenting authors (one for each paper) will be provided two nights of accommodation at the Vision Hotel close to Beihang University. Announcement of accepted papers will be made July 29, 2012.

Jun CAI, City University of Hong Kong

Jaime CASASSUS, Universidad Catolica de Chile

Guotai CHI, Dalian University of Technology

Alex FRINO, University of Sydney

Joseph FUNG, Hong Kong Baptist University

Yinhai HUA, Nanjing University of Finance and Economics

Jangkoo KANG, KAIST, Seoul, Korea

Tong Suk KIM, KAIST, Seoul, Korea

Donald LIEN, University of Texas at San Antonio

Peng LIU, Cornell University

Yiuman TSE, University of Texas at San Antonio

Giorgio VALENTE, University of Essex

Changyun WANG, Renmin University of China

Robert WEBB, University of Virginia

Chongfeng WU, Shanghai Jiaotong University

Jian YANG, University of Colorado

Tags - conference , futures , derivative

Tags - volatility , data , forecasting , yield , risk , nonlinear

Should we? I don't think so, the black scholes is just a weapon, it is the person who use it improperly should be blamed instead. This infographic is a simple defense of the Black Scholes model.

Tags - black scholes , crisis , credit

Tags - risk, , crisis, , data, , hedgefund

First of all it is important to understand the formula of the Stochastic Oscillator:

Main Stochastic (%K) = 100 * (Closing Price - Lowest Close of Last 5 Bars) / (Highest High of Last 5 Bars - Lowest Close of Last 5 Bars)

Signal Stochastic (%D) = 3-Period Exponential Moving Average of the Main Stochastic

From the formula we can derive that the main stochastic is showing us the relative location of current price in relation to the range of last 5 bars. Low readings indicate that price is near a support level (the lowest point of the range) and high readings indicate that price is near a resistance level (the highest point of the range).

Most traders enter trades when the main stochastic crosses the signal stochastic line - when a cross is from below it is a long signal, and when the cross is from below it is a short signal.

Another trading method is to enter trades when the Stochastic Oscillator crosses the 60 level (long trade), and when it crosses the 40 level (for shotr trade). It is a trend-following approach that works well in stock charts with strong trends.

It is remarkable that an indicator that was developed 60 years ago is still useful and still generates powerful signals to this day, on many stocks and commodities.

One can also improve the formula of the Stochastic to take into account ranges that are shifting: Channels instead of parallel trends. The improved formula would show the location of price in relation to the boundaries of regression channel, giving much more accurate signals that take into account the trend as well, and not just flat high and low.

We highly recommend getting to know this indicator and mastering the trading systems presented here. It can provide very accurate signals, both trend-following and reversal signals, and can provide you with trading edge.

Tags - trading , stochastic , oscillator , average

A key ingredient in these research areas is proper and clean (historical and up-to-date) intra-daily data. On the web there are various resources available, but most of them require a relatively high fee. Other solutions require the use of a specific software. However, there are ways to retrieve intra-daily data for free using Google Finance and also without any software.

If you are familiar with MatLab you can use parts of the package 'Volume Weighted Average Price from Intra-Daily Data' by Semin Ibisevic referenced at Qoppa Investment Society. This package allows you to

(1) retrieve intra-daily stock price data from Google Finance; (2) calculate the VWAP at the end of each trading day; and (3) transform intra-daily data to a daily format. It is a relatively flexible function as it only requires the user to input the ticker symbol and the exchange where the security is listed on. Additionally, the user can define the frequency of the data (1 second or higher) and the period (for instance past 10 days).

If you don't have Matlab you can replicate parts of the code manually. The package above connects with Google Finance and downloads a spreadsheet of intra-daily data consisting of the prices high, open, low, close and volume from: Google Finance get price 1.

You can adjust this to your own preferences by 'seeing' the address as: Google Finance get price 2, where

Hint: to track these inputs, for instance for the Dow Jones Industrial Average, you search the security of interest at Google Finance and then you can find at the top: (INDEXDJX:.DJI) which obviously refers to (EXCHANGE:TICKER).

In a world with increasing competition, such solutions are an handy tool to easier the life of a researcher.

Scholtus, Martin L. and Van Dijk, Dick J. C., High-Frequency Technical Trading: The Importance of Speed (February 28, 2012). Tinbergen Institute Discussion Paper 12-018/4. Available at SSRN: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2013789.

Ibisevic, Semin. Volume Weighted Average Price from Intra-Daily Data, 2012, MatLab File Exchange. Available online at: http://www.mathworks.com/matlabcentral/fileexchange/36115-volume-weighted-average-price-from-intra-daily-data.

Tags - data , historical , google , intraday

Tags - optimization , algorithm , machine-learning , julia

Tags - volatility , asymmetric , bid-ask , crisis , r , mathematics

Spent this weekend searching for opportunities both in UK and China, with emphasis on assistant professor at finance department. The results are really surprising, I heard the salary in UK is low, but never thought it is soooooooooo low, are you kidding me, UK? Except London Business School, other top universities pay extremely low, with a range of 30k GBP to 50k GBP for junior lecturer (equivalent to assistant professor) based on advertisement.

As a comparison, below is a salary list for those top mainland universities in China in GBP (econ for economics department, fin for finance department, all for assistant professor):

Shandong U (econ) 25k

Wuhan U (econ) 26k

Renmin Business School (fin) 40k

Shandong (econ) 20k

THU Shenzhen (fin) 50k

CQTBU (econ) 15k

PKU SOE (econ) 24k

SWUFE (econ) 25k

Renmin Labor and HR (econ) 32k

Fudan SOE (econ) 35k

ZJU (econ/fin) 35k

SHUFE (fin) 35k

THU SEM (econ/fin) 36k

Renmin Hanqing (fin) 39k

PKU Guanghua (econ/fin) 40k

PKU HSBC (econ) 40k

SWUFE (fin) 50k

PKU HSBC (fin) 50k

CEIBS (fin) 65k

SAIF (fin) 68k

CKGSB (econ) 125k

CKGSB (fin) 190k

Many universities in China pay similarly as in UK, I wish this post is an April fools day joke, but it is TRUE. I know we can't just compare salary when choosing a university, but still, are you kidding me, UK?

Please leave a comment if my number isn't correct.

Tags - career , salary , professor , china , uk

In the aftermath of the Credit Crisis it became popular to blame quants and mathematics for the Credit Crisis. In November, 2008, a former French prime minister, Michel Rocard, wrote in

As the dust settled, The Financial Crisis Inquiry Comission Report gave a more thoughtful analysis. They mentioned maths and quants, but only in passing. Their conclusion was that there had been a “systemic breakdown in accountability and ethics”, which had resulted in lax regulation and excessive borrowing.

In one respect the FCIC conclusions are positive for mathematicians, the Crisis wasn’t their fault. On the other hand, if the problems were rooted in ethics, then surely maths has no role in preventing future Crisis. Maths is just another tool, like a spread sheet or double entry bookkeeping. This is pretty depressing for the heirs of Newton, Euler, Riemann, Poincaré and Kolmogorov.

The mathematical study of probability is usually thought to have begun in the mid-sixteenth century, with Cardano’s

Quotation

These facts contribute a great deal to understanding but hardly anything to practical play.^{1}

Cardano’s work was ignored for centuries, the problem was, despite Cardano’s status as a mathematician, his ‘Book on Games of Chance’ didn’t fit in to what modern mathematicians regard as proper mathematics. The fact is that Cardano did not see his work on probability as principally a mathematical work, but as an investigation of the

A more orthodox study of probability was James Bernoulli’s ‘Art of Conjecturing’, however, even the great Bernoulli’s text becomes somewhat incoherent for the modern reader. In the final section Bernoulli considered situations where the sum of probabilities could be greater than one

Quotation

While traditional histories of mathematical probability start with Pierre Fermat, Pascal and Huygens because they give what are from the modern point of view correct frequentist solutions to the problems of division and expectations in games of chance …the foundations of Huygens’s method (…) was not chance (frequentist probability), but rather *sors *(expectation) in so far as it was involved in implicit contracts and the just treatment of partners.^{4}

The historical evidence seems to point to mathematical probability emerging out of the ethical examination of commercial transactions. During the eighteenth century, as science became focussed on the mechanics of physical objects, probability became associated with counting relative frequencies, a physical phenomenon, and its roots in the ethics of exchange were lost.

The ethical approach to probability of Bernoulli, Huygens and Cardano had a long pedigree. The Greek philosopher Aristotle never used mathematics in relation to physics, but he did in the analysis of the justice of exchange in his most famous study of morality, Nicomachean Ethics

Quotation

the just price of things is not fixed with mathematical precision, but depends on a kind of estimate^{6}

and, later,

Quotation

The judgement of the value of a thing in exchange seldom or never can be made except through conjecture or probable opinion, and not so precisely, or as if understood and measured by one invisible point, but rather as a fitting latitude within which the diverse judgements of men will differ in estimation.^{7}

These opinions are revolutionary in the development of western science

Quotation

[it is] foolish to accept probable reasoning from a mathematician and to demand from a rhetorician scientific proofs.^{9}

By exploring the ethics of exchange through mathematics, these medieval scholars cleared the path for physicists to start using probability and statistics.

This was the background to Cardano’s Book on Chance, and it is captured when he says

Quotation

The most fundamental principle of all in gambling is simply equal conditions, e.g., of opponents, of bystanders, of money, of situation, of the dice box, and of the die itself. To the extent to which you depart from that equality, if it is in your opponent’s favour, you are a fool, and if in your own, you are unjust.^{10}

Cardano’s point, which goes back to Aristotle, is that a stake should equal the expected winnings.

This explains Bernoulli’s probabilities that did not add up to one, he was defining a probability as a set of factors that made the expected winnings equal to the stake. These types of situations are common in modern commercial gambling, where the sum of the odds offered to a gambler provide the bookkeeper with a certain profit, what would be call an arbitrage in finance.

Today Financial Mathematics is built on the Fundamental Theorem of Asset Pricing, a mathematical theorem that emerged in the late 1970s out of the Black-Scholes equation. The first statement of the Theorem is

Quotation

A market is arbitrage free if and only if a martingale measure exists.

Quotation

Fairness is based on equality.

The association between mathematics and morality had all but disappeared in 1812 when Laplace published his ‘Analytic Probability Theory’ and gave an argument as to why mathematical (frequentist) expectation was a better guide than the moral expectation of Cardano and Bernoulli. About the same time, the English philosopher Jeremy Bentham introduced the concept of ‘utility’ into political economy from mathematics, and then, in 1836, the philosopher John Stuart Mill argued that economics

Quotation

is concerned with [man] solely as a being who desires to possess wealth, and who is capable of judging the comparative efficacy of means for obtaining that end.^{11}

Not all economists bought into ‘Max U’, some were less inspired by economic theory, what people ought to do, and more by practice, what people actually do. In particular an experiment blew ‘Max U’ out of the water, the ‘Ultimatum Game’. The game is based on an experimenter, two participants and a sum of money. The experimenter gives all the money to the first player, who proposes how to share the money with the second participant. The division is made if the second participant accepts the split, but neither player gets anything if the first player’s proposal is rejected.

According to Max U, the second player should accept any split of the pot, they are getting something for nothing. However, the results of the experiments on adults are that if the money is not split equally, or close to, then the second player rejects the offer. Research has shown that chimpanzees are rational maximisers while the willingness of the second player to accept an offer is dependent on age or culture. Older people from societies where trade and exchange plays a significant role are more likely to demand a fairer split of the pot than young children or adults from isolated communities.

Maximising utility, the main method of academic economics, is a selfish, greedy approach to making financial decisions. When quants price derivatives using no-arbitrage arguments they are using a method that places fairness at the heart of the markets. Mathematics does have a role in maintaining ethics in the markets.

1 David [1962(1998)], p 58], quoting from Chapter 9 of the

2 Bellhouse [2005]

3 Sylla [2006, p 27]

4 Sylla [2006, p 28]

5 Aristotle [1999, Book V]

6 Aquinas [1947, Second part of the second part, Q77, 1]

7 Kaye [1998, p 124]

8 Hadden [1994], Crosby [1997], Kaye [1998]

9 Aristotle [1999, Book 1, 3]

10 Bellhouse [2005] quoting from Chapter 6 of the Liber

11 Persky [1995, quoting Mill, p 223]

12 Murnighan and Saxon [1998], Henrich et al. [2006], Jensen et al. [2007]

Thomas Aquinas. Summa Theologica. Benziger Bros, 1947.

Aristotle. Nicomachean Ethics, translated by W. D. Ross. Batoche, 1999.

D. Bellhouse. Decoding Cardano’s Liber de Ludo Aleae. Historia Mathematica, 32:180–202, 2005.

A. W. Crosby. The Measure of Reality. Cambridge University Press, 1997.

F.N. David. Games, Gods and Gambling, A history of Probability and Statistical Ideas. Charles Griffin & Co (Dover), 1962(1998).

R. W. Hadden. On the Shoulders of Merchants: Exchange and the Mathematical Conception of Nature in Early Modern Europe. State University of New York Press, 1994.

J. Henrich et al. Costly punishment across human societies. Science, 312:1767–1770, 2006.

K. Jensen, J. Call, and M. Tomasello. Chimpanzees are rational maximizers in an ultimatum game. Science, 318:107–108, 2007.

J. Kaye. Economy and Nature in the Fourteenth Century. Cambridge University Press, 1998.

J. K. Murnighan and M. S. Saxon. Ultimatum bargaining by children and adults. Journal of Economic Psychology, 19:415–445, 1998.

J. Persky. Retrospectives: The ethology of Homo economicus. The Journal of Economic Perspectives, 9(2):221–231, 1995. E. D. Sylla. Commercial arithmetic, theology and the intellectual foundations of Jacob Bernoulli’s Art of Conjecturing. In G. Poitras, editor, Pioneers of Financial Economics: contributions prior to Irving Fisher, pages 11–45. Edward Elgar, 2006.

Tags - mathematics , crisis , quant