26. All else being equal, which of the following options would cost more than plain vanilla options?

I. lookback options

II. barrier options

III. Asian options

IV. chooser options

A. I only

B. I & IV

C. II & III

D. I, III & IV

27. Consider an asset worth USD 1 million whose 95th percentile VaR is USD 100,000 (computed using the parametric method assuming the normal distribution). Suppose the bid-ask spread on the asset has a mean of USD 0.10 and a standard deviation of USD 0.30. What is the 95th percentile liquidity adjusted VaR assuming the market risk VaR and the liquidity risk piece are uncorrelated?

A. USD 200,000

B. USD 344,000

C. USD 444,000

D. USD 688,000

28. Given the following portfolio of bonds:

What is the value of the portfolio's DV01 (Dollar value of 1 basis point)?

A. 8,019

B. 8,294

C. 8,584 

D. 8,813

29. A risk manager believes that there is some probability that ABC Company's bond rating will be revised downward from A to A-. She wants to obtain an estimate of the change in value of the company's bond if such a change takes place. Which of the following approaches should she not use to estimate the impact of the rating change on the price of the company's bond?

A. Multiply the change in yield spread resulting from the rating change by the modified duration of the bond using the average yield to maturity or the option adjusted spread, by bond rating class.

B. Estimate the new forward curve after the rating change, compute the price of the bond using the new curve for the remaining cash flows, and compare that to the original bond price.

C. Empirically estimate historical price changes following a rating change on a large sample of bonds across different rating classes using an "event study" methodology.

D. Calculate the price change of the bond the last time a rating change occurred and use it as your estimate.

30. A first-to-default basket credit default swap is a credit derivative that:

A. Entails a number of reference entities and provides a payoff only when the first reference entity defaults.

B. Entails a number of reference entities and provides a payoff only when the first entity's recovery rate is higher than the rest of the entities in the swap.

C. Provides a payoff when the first entity of the credit default swap issues securities.

D. Provides a payoff when the first entity of the credit default swap issues a basket option to repurchase the issuers' bonds.

26. All else being equal, which of the following options would cost more than plain vanilla options?

ffice:smarttags" />I. lookback options

II. barrier options

III. Asian options

IV. chooser options

A. I only

B. I & IV

C. II & III

D. I, III & IV

Correct answer is B

I is correct. The payoff on look-back options depends on the maximum or minimum underlying price achieved during the life of the option. The option holder is guaranteed the most favorable rate during the life of the option. As a result, the premium is substantially higher than plain vanilla options.fficeffice" />

II is incorrect. A barrier option is extinguished or created only when the barrier is touched. For example, an up-and-in call option would only be created if at some point during the option's life the price of the underlying exceeded the barrier; if it failed to do so it could not be exercised regardless of whether it finished in-the-money or not. Similarly, a down-and-out put option would automatically be extinguished if, during the option's life, the underlying asset's price fell below the barrier. Barrier options are always less expensive than plain vanilla options as there is always a probability that the options will be knocked out or not be knocked in.

III is incorrect. The pay-off for Asian options is based on the average price of the underlying asset over the life of the option and not a set strike price.  Asian options are cheaper than plain vanilla options as average prices are less volatile than day-to-day prices.

IV is correct. A chooser option has the feature that after a specified period of time, the holder can choose to decide whether the option is a put or call. As a result of this increased flexibility, chooser options are more expensive than plain vanilla options. 

Reference: John Hull, Options Futures and Other Derivatives, 6th edition (New York: Prentice Hall, 2006), Chapter 22.

27. Consider an asset worth USD 1 million whose 95th percentile VaR is USD 100,000 (computed using the parametric method assuming the normal distribution). Suppose the bid-ask spread on the asset has a mean of USD 0.10 and a standard deviation of USD 0.30. What is the 95th percentile liquidity adjusted VaR assuming the market risk VaR and the liquidity risk piece are uncorrelated?

A. USD 200,000

B. USD 344,000

C. USD 444,000

D. USD 688,000

Correct answer is C

If the VaR is USD100,000, the liquidity piece can be estimated from the mean and std dev of the spread as 

With no correlation to the market risk piece, we add to get (b).

Reference:  Culp, Chapter 17

28. Given the following portfolio of bonds:

What is the value of the portfolio's DV01 (Dollar value of 1 basis point)?

A. 8,019

B. 8,294

C. 8,584 

D. 8,813

Correct answer is C

The portfolio dollar duration of a basis point (DV01)

       = (portfolio modified duration X market value of portfolio)/10,000

The portfolio modified duration is obtained by taking the weighted average of the modified duration of the bonds in the portfolio.

Mathematically, it is as follows:      w1D1 + w2D2 + w3D3 +…+wkDk,

where wi = market value of bond i/market value of the portfolio

           Di = modified duration of bond i

           K = number of bonds of the portfolio.  

Based on the above, the market values are as follows:

bond A = 101.43 x 3,000,000/100 = 3,042,900

bond B = 84.89 x 5,000,000/100 = 4,244,500

bond C = 121.87 x 8,000,000/100 = 9,749,600

Total market value of the portfolio = 3,042,900 + 4,244,500 + 9,749,600  = 17,037,000      

Portfolio modified duration is calculated as follows:

(3,042,900/17,037,000)2.36 + (4,244,500/17,037,000)4.13 + (9,749,600/17,037,000)6.27 = (0.1786)2.36 + (0.2491)4.13 + (0.5723)6.27

                              = 0.4215 + 1.0289 + 3.5881 = 5.0385

Therefore, the portfolio dollar duration of a basis point (DV01) is obtained as follows:

       (5.0385 x 17,037,000)/10,000 = 8,584       

Reference: Bruce Tuckman, Fixed Income Securities, 2nd edition (New York: Wiley, 2002), Chapters 5&6.

29. A risk manager believes that there is some probability that ABC Company's bond rating will be revised downward from A to A-. She wants to obtain an estimate of the change in value of the company's bond if such a change takes place. Which of the following approaches should she not use to estimate the impact of the rating change on the price of the company's bond?

A. Multiply the change in yield spread resulting from the rating change by the modified duration of the bond using the average yield to maturity or the option adjusted spread, by bond rating class.

B. Estimate the new forward curve after the rating change, compute the price of the bond using the new curve for the remaining cash flows, and compare that to the original bond price.

C. Empirically estimate historical price changes following a rating change on a large sample of bonds across different rating classes using an "event study" methodology.

D. Calculate the price change of the bond the last time a rating change occurred and use it as your estimate.

Correct answer is D

This approach is not reasonable for several reasons, including the total lack of information given about how to set a volatility input or distribution type.  More importantly, the price change of the bond for the last rating change might well correspond to a different kind of migration (eg, AAA to A) than the one being contemplated now, and possibly, there has never a prior ratings change in this series.

Reference: Arnaud de Servigny and Olivier Renault, Measuring and Managing Credit Risk. Chapter 2.

30. A first-to-default basket credit default swap is a credit derivative that:

A. Entails a number of reference entities and provides a payoff only when the first reference entity defaults.

B. Entails a number of reference entities and provides a payoff only when the first entity's recovery rate is higher than the rest of the entities in the swap.

C. Provides a payoff when the first entity of the credit default swap issues securities.

D. Provides a payoff when the first entity of the credit default swap issues a basket option to repurchase the issuers' bonds.

Correct answer is A

In a basket credit default swap, there a number of reference entities and the swap only provides a payoff when the first reference entity defaults.

Reference: René Stulz, Risk Management & Derivatives.  Chapter 18.