Bionic Turtle

[Learn] Exotic Friday [practice, market]

2009-11-06T21:24:40+00:00

Hull 22.09. How can the value of a forward start put option on a non-dividend-paying stock be calculated if it is agreed that the strike price will be 10% greater than the stock price at the time the option starts?

Hull 22.11. Explain why delta hedging is easier for Asian options than for regular options.

[my adds]

22.11b. What are the different types of Asian options?
22.11c. What type of average makes pricing the Asian easier?
22.11d. How will the price of an Asian average price call compare to a “plain vanilla” European call option, assuming the inputs are otherwise equivalent?

Hull 22.18. What is the value of a derivative that pays off $100 in 6 months if the S&P 500 index is greater than 1,000 and zero otherwise? Assume that the current level of the index is 960, the risk-free rate is 8% per annum, the dividend yield on the index is 3% per annum, and the volatility of the index is 20%.

[my adds]

22.18b. What types of binary options are possible?
22.18c. Explain the logic of the pricing formula for a Binary option (hint: what is the PD in Merton model?)
22.18d. Create a synthetic long position in an asset-or-nothing call by using a regular European call option.

Hull 22.19. In a 3-month down-and-out call option on silver futures the strike price is $20 per ounce and the barrier is $18. The current futures price is $19, the risk-free interest rate is 5%, and the volatility of silver futures is 40% per annum. Explain how the option works and calculate its value. What is the value of a regular call option on silver futures with the same terms? What is the value of a down-and-in call option on silver futures with the same terms?

Answers

Hull 22.09 here in forum or here in wiki
Hull 22.11 here in forum or here in wiki
Hull 22.18 here in forum or here in wiki or here in spreadsheet
Hull 22.19 here in forum or here in wiki or here in spreadsheet

[Learn] Exchange option [practice, market]

2009-11-05T20:34:52+00:00

An FRM candidate will *not* need to price an exchange option; this is just to illustrate - David

Hull.22.12 Calculate the price of a 1-year European option to give up 100 ounces of silver in exchange for 1 ounce of gold. The current prices of gold and silver are $380 and $4, respectively; the risk-free interest rate is 10% per annum; the volatility of each commodity price is 20%; and the correlation between the two prices is 0.7. Ignore storage costs.

[my adds]

22.12b. Which given input assumption is not used?
22.12c. (hard) Explain the volatility input into d1.

Answer here in forum or here in wiki or here in spreadsheet

[Learn] Barriers on hump day [practice, market]

2009-11-04T20:31:52+00:00

Hull 22.03. Consider a chooser option where the holder has the right to choose between a European call and a European put at any time during a 2-year period. The maturity dates and strike prices for the calls and puts are the same regardless of when the choice is made. Is it ever optimal to make the choice before the end of the 2-year period? Explain your answer.

Hull 22.07. Explain why a down-and-out put is worth zero when the barrier is greater than the strike price.

Hull 22.13. Is a European down-and-out option on an asset worth the same as a European down-and-out option on the asset’s futures price for a futures contract maturing at the same time as the option?

Hull 22.16 Does a down-and-out call become more valuable or less valuable as we increase the frequency with which we observe the asset price in determining whether the barrier has been crossed? What is the answer to the same question for a down-and-in call?

Hull 22.17 Explain why a regular European call option is the sum of a down-and-out European call and a down-and-in European call. Is the same true for American call options?

Answers

Hull.22.03 here in forum or here in wiki
Hull 22.07 here in forum or here in wiki
Hull 22.13 here in forum or here in wiki
Hull 22.16 here in forum or here in wiki
Hull 22.17 here in forum or here in wiki

[Tools] 2009 9.b Current Issues (UBS, Stress, Lo) - sample

2009-11-04T17:53:27+00:00

Shareholder Report on UBS’s Write‐Downs; Why Banks Failed the Stress Test; Andrew Lo's Testimony on Hedge Funds

*[Tools] 2009 9.b Current Issues (UBS, Stress, Lo)

2009-11-04T17:51:27+00:00

Shareholder Report on UBS’s Write‐Downs; Why Banks Failed the Stress Test; Andrew Lo's Testimony on Hedge Funds

[Learn] Lookback options [practice, market]

2009-11-03T21:57:33+00:00

Hull 22.02. Describe the payoff from a portfolio consisting of a lookback call and a lookback put with the same maturity.

22.15. Does a floating lookback call become more valuable or less valuable as we increase the frequency with which we observe the asset price in calculating the minimum?

[my adds]

22.15b. What are the four types (variations) of a lookback option?
22.15c. Can the intrinsic value of a floating lookback call ever be negative?

Answer here in forum or here in wiki

[Learn] Chooser option [practice, market]

2009-11-02T22:31:03+00:00

Hull 22.01. Explain the difference between a forward start option and a chooser option.

[my adds]

22.01b. Assume a European chooser option where stock price is $10, strike price is $10, volatility is 20%, dividend yield is 0%, and risk-free rate is 4%. The choice can be made within the next six months (T1 = 0.5 years) and the option will expire in one year (T2 = 1.0 year). What is a synthetic (portfolio) equivalent to the chooser option?

22.01c. What is the value of the chooser option? (an FRM candidate does *not* need to value a chooser)

22.01d. How is a chooser both similar to, and different from, an option straddle?

22.01e. How does the value of the chooser compare to an equivalent straddle?

Answer here in forum or here in wiki

[Learn] Hull 20.07, Netting [practice, credit]

2009-10-31T01:45:20+00:00

Did you realize the FRM refers to at least three types of netting? Do you know them? - David

Hull 20.7. Describe how netting works. A bank already has one transaction with a counterparty on its books. Explain why a new transaction by a bank with a counterparty can have the effect of increasing or reducing the bank’s credit exposure to the counterparty.

[my adds]

20.7b. If Firm A owes $5 million to Firm B in one contract but Firm B owes $7 million to Firm A in another contract, what is Firm B’s CREDIT EXPOSURE to Firm A (i) without netting and (ii) with netting

20.7c. What are the different types of “netting” and what are the differences?

20.7d. (A variation of this question appeared in a previous exam!) A typical master netting agreement as established by the ISDA will contain each of the following EXCEPT:

a. Expected Credit Exposure (ECE)
b. Credit provisions
c. List of obligations
d. Contractual boilerplate

Answer here in forum or here in wiki

[Tools] 2009 9.a.ii Current Issues (NR, Securitization) - sample

2009-10-30T17:31:08+00:00

Observations on Recent Market Turbulence (March 2008); Northern Rock: Executive Summary; John Martin's Primer on the Role of Securitization in the Credit Market Crisis of 2007. (9.a.i and 9.a.ii share the same 80-page PowerPoint deck).

*[Tools] 2009 9.a.ii Current Issues (NR, Securitization)

2009-10-30T17:28:04+00:00

*[Spreadsheets] 9.a2 Gorton’s Repo

2009-10-30T00:56:04+00:00

*[Spreadsheets] 9.a.1 ABX Index

2009-10-30T00:48:26+00:00

[Tools] 2009 9.a.i Current Issues (Gorton, Rajan) - sample

2009-10-29T20:37:10+00:00

1. Gary Gorton: Information, Liquidity, and the (Ongoing) Panic of 2007; and 2. Raghuram Rajan: Has Financial Development Made The World Riskier

*[Tools] 2009 9.a.i Current Issues (Gorton, Rajan)

2009-10-29T20:33:16+00:00

1. Gary Gorton: Information, Liquidity, and the (Ongoing) Panic of 2007; and 2. Raghuram Rajan: Has Financial Development Made The World Riskier

[Learn] Real-world vs. risk-neutral default intensities [practice, credit]

2009-10-29T21:25:54+00:00

20.6 [I replaced source with my own] Assume the same average cumulative default rates as given by in Hull’s Table 22.1 (1970-2006, Source: Moody’s):

20.6a. What is the average historical default intensity for a 10-year B-rated obligor?
20.6b. Assume the 7-year swap rate is 5.398% and the average yield on an Aa-rated bond is 5.7420% (further, assume the risk free rate is the swap rate minus 10 basis points). The recovery rate is 40%. For the 7-year Aa-rated bond, what is the (i) the real-world historical default intensity and (ii) risk-neutral default intensity from bond prices?
20.6c. Do we expect these two default intensities to be equal?
20.6d. If the 7-year Aa-rated bond has an average spread over Treasuries of 100 basis points, and the spread of the risk-free rate over Treasuries is 42 basis points, what is the expected excess return on the bond?

Answer here in forum or here in wiki

[Learn] Hazard rate [practice, credit]

2009-10-28T19:29:04+00:00

Hull 20.5. Explain the difference between an unconditional default probability density and a default intensity.

[my adds]

The following table (extract from Hull’s Table 20.1) displays actual average cumulative default rates from 1970 to 2009:

20.5b. For a B-rated bond, what is the 5-year unconditional default probability?
20.5c. For a B-rated bond, what conditional PD in the fifth year (i.e., year 5 conditional PD)?
20.5d. What is the difference between (i) conditional PD, (ii) hazard rate and (iii) default intensity?
20.5e. Which continuous probability distribution (in the assigned Rachev: Fat-tailed and Skewed Asset Return Distributions) characterizes the hazard rate?

Answer here in forum or here in wiki or here in spreadsheet

[Learn] Recovery rates [practice, credit]

2009-10-27T21:25:19+00:00

Hull 20.3. Should researchers use real-world or risk-neutral default probabilities for (a) calculating credit value at risk and (b) adjusting the price of a derivative for defaults?

20.4. How are recovery rates usually defined?

[my adds]

20.4b. What is arguably the most important determinant of recovery?
20.4c. According to J. Hull, what is the historical relationship between default rates and recovery rates?
20.4d. Which distribution is popular for modeling recovery?
20.4e. Do the credit risk portfolio models generally assume a relationship (dependence or correlation) between PD (or EDF) and recovery (or LGD)?
20.4f. In Basel II’s standardized approach to credit, how is recovery parameterized? This approach is more consistent with which ratings philosophy—S&P or Moody’s?
20.4g. In Basel II’s Foundation IRB, how is recovery parameterized?
20.4h. In Basel II’s Advanced IRB, how is recovery parameterized?
20.4i. Does Basel II’s IRB attempt to factor economic conditions?

Answers

Hull 20.03 here in forum or here in wiki
Hull 20.04 here in forum or here in wiki

[Learn] Hull 20.01 (default intensity) [practice, credit]

2009-10-26T17:21:02+00:00

20.1. The spread between the yield on a 3-year corporate bond and the yield on a similar risk-free bond is 50 basis points. The recovery rate is 30%. Estimate the average default intensity per year over the 3-year period.

[my add]
20.1b. Assume the riskfree rate is 4%, the bond pays a 4% semi-annual coupon with face value of $100, and all rates are given in (discrete) semi-annual compound frequency. What is the more exact estimate of probability of default (PD)?

20.2. Suppose that in Problem 22.1 the spread between the yield on a 5-year bond issued by the same company and the yield on a similar risk-free bond is 60 basis points. Assume the same recovery rate of 30%. Estimate the average default intensity per year over the 5-year period. What do your results indicate about the average default intensity in years 4 and 5?

Answer here in forum or here in wiki or here in spreadsheet

[Learn] More GARCH [practice, quant]

2009-10-23T18:54:20+00:00

Hull 19.10. The parameters of a GARCH(1,1) model are estimated as omega = 0.000004, alpha = 0.05, and beta = 0.92. What is the long-run average volatility and what is the equation describing the way that the variance rate reverts to its long-run average? If the current volatility is 20% per year, what is the expected volatility in 20 days (252 trading days per year)?

Hull 19.11. (Much more difficult than exam. You can skip). Suppose that the current daily volatilities of asset X and asset Y are 1.0% and 1.2%, respectively. The prices of the assets at close of trading yesterday were $30 and $50 and the estimate of the coefficient of correlation between the returns on the two assets made at this time was 0.50. Correlations and volatilities are updated using a GARCH(1,1) model. The estimates of the model's parameters are alpha = 0.04 and beta = 0.94. For the correlation omega = 0.000001, and for the volatilities omega = 0.000003. If the prices of the two assets at close of trading today are $31 and $51, how is the correlation estimate updated?

19.12. Suppose that the daily volatility of the FTSE 100 stock index (measured in pounds sterling) is 1.8% and the daily volatility of the dollar/sterling exchange rate is 0.9%. Suppose further that the correlation between the FTSE 100 and the dollar/sterling exchange rate is 0.4. What is the volatility of the FTSE 100 when it is translated to US dollars? Assume that the dollar/sterling exchange rate is expressed as the number of US dollars per pound sterling. (Hint: When Z = XY, the percentage daily change in Z is approximately equal to the percentage daily change in X plus the percentage daily change in Y.)

Answers:

Hull 19.10 here in forum or here in wiki or here in spreadsheet
Hull 19.11 here in forum or here in wiki or here in spreadsheet
Hull 19.12 here in forum or here in wiki or here in spreadsheet

[Learn] EWMA correlation [practice, quant]

2009-10-22T17:35:01+00:00

Hull 19.7. The most recent estimate of the daily volatility of the US dollar/sterling exchange rate is 0.6% and the exchange rate at 4 p.m. yesterday was 1.5000. The parameter lambda in the EWMA model is 0.9. Suppose that the exchange rate at 4 p.m. today proves to be 1.4950. How would the estimate of the daily volatility be updated?

Hull 19.8. Assume that S&P 500 at close of trading yesterday was 1,040 and the daily volatility of the index was estimated as 1% per day at that time. The parameters in a GARCH(l, 1) model are omega = 0.000002 (2 E-06), alpha = 0.06, and beta = 0.92. If the level of the index at close of trading today is 1,060, what is the new volatility estimate?

[my add]
19.08b. What is the forecast of daily volatility 10 days forward?

Hull 19.9. Suppose that the daily volatilities of asset A and asset B, calculated at the close of trading yesterday, are 1.6% and 2.5%, respectively. The prices of the assets at close of trading yesterday were $20 and $40 and the estimate of the coefficient of correlation between the returns on the two assets was 0.25. The parameter lambda used in the EWMA model is 0.95.

(a) Calculate the current estimate of the covariance between the assets.
(b) On the assumption that the prices of the assets at close of trading today are $20.5 and $40.5, update the correlation estimate

Answers

Hull 19.07 here in forum or here in wiki
Hull 19.08 here in forum or here in wiki
Hull 19.09 here in forum or here in wiki