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principles of finance

Questions and Answers of Principles Of Finance

17.24. A financial institution has the following portfolio of over-the-counter options on sterling:A traded option is available with a delta of 0.6, a gamma of 1.5, and a vega of 0.8.(a) What
23.25. Table 23.7 shows the five-year iTraxx index was 77 basis points on January 31, 2008.Assume the risk-free rate is 5% for all maturities, the recovery rate is 40%, and payments are quarterly.
23.24. The 1-, 2-, 3-, 4-, and 5-year CDS spreads are 100, 120, 135, 145, and 152 basis points, respectively. The risk-free rate is 3% for all maturities, the recovery rate is 35%, and payments are
23.23. Suppose that (a) the yield on a five-year risk-free bond is 7%, (b) the yield on a five-year corporate bond issued by company X is 9.5%, and (c) a five-year credit default swap providing
23.22. Explain how you would expect the returns offered on the various tranches in a synthetic CDO to change when the correlation between the bonds in the portfolio increases.
23.21. Assume that the hazard rate for a company in a year is λ and the recovery rate is R. The risk-free interest rate is 5% per annum. Default always occur halfway through a year. The spread for a
23.20. Suppose that the risk-free zero curve is flat at 6% per annum with continuous compounding and that defaults can occur at times 0.25, 0.75, 1.25, and 1.75 years in a twoyear plain vanilla
23.19. Does valuing a CDS using real-world default probabilities rather than risk-neutral default probabilities overstate or understate its value? Explain your answer.
23.18. Why is there a potential asymmetric information problem in credit default swaps?
23.17. “The position of a buyer of a credit default swap is similar to the position of someone who is long a risk-free bond and short a corporate bond.” Explain this statement.
23.16. Explain how forward contracts and options on credit default swaps are structured.
23.15. A company enters into a total return swap where it receives the return on a corporate bond paying a coupon of 5% and pays LIBOR. Explain the difference between this and a regular swap where 5%
23.14. Verify that, if the CDS spread for the example in Tables 23.2 to 23.5 is 100 basis points, the hazard rate is 1.63% per year. How does the hazard rate change when the recovery rate is 20%
23.13. Show that the spread for a new plain vanilla CDS should be 1 - R times the spread for a similar new binary CDS, where R is the recovery rate.
23.12. How is the recovery rate of a bond usually defined? What is the formula relating the payoff on a CDS to the notional principal and recovery rate?
23.11. How does a five-year nth-to-default credit default swap work? Consider a basket of 100 reference entities where each reference entity has a probability of defaulting in each year of 1%. As the
23.10. What is the credit default swap spread in Problem 23.8 if it is a binary CDS.
23.9. What is the value of the swap in Problem 23.8 per dollar of notional principal to the protection buyer if the credit default swap spread is 150 basis points?
23.8. Suppose that the risk-free zero curve is flat at 7% per annum with continuous compounding and that defaults can occur halfway through each year in a new five-year credit default swap. Suppose,
23.7. Explain why a total return swap can be useful as a financing tool.
23.6. Explain the difference between risk-neutral and real-world default probabilities.
23.5. Explain what a first-to-default credit default swap is. Does its value increase or decrease as the default correlation between the companies in the basket increases? Explain why.
23.4. Explain how a cash CDO and a synthetic CDO are created.
23.3. Explain how a credit default swap is settled.
23.1. How does a binary credit default swap differ from a regular credit default swap?
22.26. What is the relationship between a regular call option, a binary call option, and a gap call option?
22.25. Outperformance certificates (also called “sprint certificates,” “accelerator certificates,” or“speeders”) are offered to investors by many European banks as a way of investing in a
22.24. All one-year LIBOR forward rates are 5% with annual compounding and the risk-free(OIS) rate is 4.6% with continuous compounding. In a five-year swap, company X pays a fixed rate of 6% and
22.20. Estimate the interest rate paid by P&G on the 5/30 swap in Business Snapshot 22.4 if (a)the CP rate is 6.5% and the Treasury yield curve is flat at 6% and (b) the CP rate is 7.5%and the
22.18. Explain why a regular European call option is the sum of a down-and-out European call and a down-and-in European call.
22.16. 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?
22.14. Suppose that the strike price of an American call option on a non-dividend-paying stock grows at rate g. Show that if g is less than the risk-free rate, r, it is never optimal to exercise the
22.13. Prove that an at-the-money forward start option on a non-dividend-paying stock that will start in three years and mature in five years is worth the same as a two-year at-the-money option
22.12. E xplain why a down-and-out put is worth zero when the barrier is greater than the strike price.
22.11. The text derives a decomposition of a particular type of chooser option into a call maturing at time T2 and a put maturing at time T1. By using put–call parity to obtain an expression for c
22.10. Suppose that c1 and p1 are the prices of a European average price call and a European average price put with strike price K and maturity T, c2 and p2 are the prices of a European average
22.8. Describe the payoff from a portfolio consisting of a floating lookback call and a floating lookback put with the same maturity.
22.6. Explain the relationship between a cancelable swap and a swap option.
22.5. Explain why IOs and POs have opposite sensitivities to the rate of prepayments.
22.4. How does an equity swap work?
22.3. List eight types of barrier options.
22.1. Explain the difference between a forward start option and a chooser option.
21.22. Use the DerivaGem software to value a European swaption that gives you the right in 2 years to enter into a 5-year swap in which you pay a fixed rate of 6% and receive floating.Cash flows are
21.21. Calculate the price of a cap on the 3-month LIBOR rate in 9 months’ time for a principal amount of $1,000. Use Black’s model and the following information:Quoted 9-month Eurodollar futures
21.20. A swaption gives the holder the right to receive 7.6% in a 5-year swap starting in 4 years.Payments are made annually. The forward swap rate is 8% with annual compounding and its volatility is
21.17. Suppose that risk-free zero rates and LIBOR forward rates are as in Problem 21.14. Use DerivaGem to determine the value of an option to pay a fixed rate of 6% and receive LIBOR on a five-year
21.16. Explain why there is an arbitrage opportunity if the implied Black (flat) volatility for a cap is different from that for a floor.
21.14. Suppose that all risk-free (OIS) zero rates are 6.5% (continuously compounded). The price of a 5-year semiannual cap with a principal of $100 and a cap rate of 8% (semiannually compounded) is
21.13. What other instrument is the same as a 5-year zero-cost collar in which the strike price of the cap equals the strike price of the floor? What does the common strike price equal?
21.12. Explain carefully how you would use (a) spot volatilities and (b) flat volatilities to value a 5-year cap.
21.10. If the yield volatility for a 5-year put option on a bond maturing in 10 years time is specified as 22%, how should the option be valued? Assume that, based on today’s interest rates, the
21.9. Consider a 4-year European call option on a bond that will mature in 5 years. The 5-year bond price is $105, the price of a 4-year bond with the same coupon as the 5-year bond is $102, the
21.7. What are the advantages of term structure models over Black’s model for valuing interest rate derivatives?
21.5. Suppose you buy a Eurodollar call futures option contract with a strike price of 97.25.You exercise when the underlying Eurodollar futures price is 98.12. What is the payoff ?
21.4. Use Black’s model to value a 1-year European put option on a 10-year bond. The current cash price of the bond is $125, the strike price is $110, the 1-year risk-free interest rate is 10% per
21.3. Explain why a swaption can be regarded as a type of bond option.
21.2. Explain the features of (a) callable and (b) puttable bonds.
20.31. The calculations for the four-index example at the end of Section 20.6 assume that the investments in the DJIA, FTSE 100, CAC 40, and Nikkei 225 are $4 million, $3 million,$1 million, and $2
20.30. Suppose that the portfolio considered in Section 20.2 has (in $000s) 3,000 in DJIA, 3,000 in FTSE, 1,000 in CAC 40 and 3,000 in Nikkei 225. Use the spreadsheet on the author’s website to
20.29. A common complaint of risk managers is that the model-building approach (either linear or quadratic) does not work well when delta is close to zero. Explain the basis for this complaint.
20.27. Suppose that in Problem 20.26 the price of silver at the close of trading yesterday was$16, its volatility was estimated as 1.5% per day, and its correlation with gold was estimated as 0.8.
20.26. Suppose that the price of gold at close of trading yesterday was $600, and its volatility was estimated as 1.3% per day. The price at the close of trading today is $596. Update the volatility
20.24. Consider a portfolio of options on a single asset. Suppose that the delta of the portfolio is 12, the value of the asset is $10, and the daily volatility of the asset is 2%. Estimate the
20.22. What is the effect of changing l from 0.94 to 0.97 in the EWMA calculations in the four-index example at the end of Section 20.6. Use the spreadsheets on the author’s website.
20.21. At the end of Section 20.6, the VaR and ES for the four-index example were calculated using the model-building approach. How do the VaR and ES estimates change if the investment is $2.5
20.20. Use the spreadsheets on the author’s website to calculate the one-day 99% VaR and ES, employing the basic methodology in Section 20.2, if the four-index portfolio considered in Section 20.2
20.19. The one-day 99% VaR is calculated for the four-index example in Section 20.2 as $253,385.Look at the underlying spreadsheets on the author’s website and calculate: (a) the oneday 95% VaR,
20.17. Suppose that the daily volatility of the FTSE 100 stock index (measured in sterling) is 1.8% and the daily volatility of the USD/GBP exchange rate is 0.9%. Suppose further that the correlation
20.16. Suppose that the daily volatilities of asset A and asset B calculated at close of trading yesterday are 1.6% and 2.5%, respectively. The prices of the assets at close of trading yesterday were
20.15. The most recent estimate of the daily volatility of the U.S. dollar–sterling exchange rate is 0.6%, and the exchange rate at 4 p.m. yesterday was 1.5000. The parameter l in the EWMA model is
20.13. Explain why the linear model can provide only approximate estimates of VaR for a portfolio containing options.
20.12. Explain how a forward contract to sell a foreign currency is mapped into a portfolio of zero-coupon bonds with standard maturities for the purposes of a VaR calculation.
20.11. The volatility of a certain market variable is 30% per annum. Calculate a 99% confidence interval for the size of the percentage daily change in the variable.
20.10. Consider a position consisting of a $100,000 investment in asset A and a $100,000 investment in asset B. Assume that the daily volatilities of both assets are 1% and that the coefficient of
20.9. Explain the difference between value at risk and expected shortfall.
20.8. A company uses an EWMA model for forecasting volatility. It decides to change the parameter l from 0.95 to 0.85. Explain the likely impact on the forecasts.
20.7. Suppose a company has a portfolio consisting of positions in stocks, bonds, foreign exchange, and commodities. Assume there are no derivatives. Explain the assumptions underlying (a) the
20.6. Suppose you know that the gamma of the portfolio in the previous quiz question is 16.2.How does this change your estimate of the relationship between the change in the portfolio value and the
20.2. Explain the exponentially weighted moving average (EWMA) model for estimating volatility from historical data.
20.1. Explain the historical simulation method for calculating VaR.
19.25. Using Table 19.2, calculate the implied volatility a trader would use for an 11-month option with a strike price of 0.98.
19.24. Consider a European call and a European put with the same strike price and time to maturity. Show that they change in value by the same amount when the volatility increases from a level, s 1,
19.23. Data for a number of stock indices are provided on the author’s website:http://www-2.rotman.utoronto.ca/~hull/data Choose an index and test whether a three standard deviation down movement
19.22. Data for a number of foreign currencies are provided on the author’s website:http://www-2.rotman.utoronto.ca/~hull/data Choose a currency and use the data to produce a table similar to Table
19.21. A futures price is currently $40. The risk-free interest rate is 5%. Some news is expected tomorrow that will cause the volatility over the next three months to be either 10% or 30%. There is
19.19. A company’s stock is selling for $4. The company has no outstanding debt. Analysts consider the liquidation value of the company to be at least $300,000 and there are 100,000 shares
19.18. Using Table 19.2, calculate the implied volatility a trader would use for an 8-month option with a strike price of 1.04.
19.17. “The Black–Scholes–Merton model is used by traders as an interpolation tool.” Discuss this view.
19.12. Option traders sometimes refer to deep-out-of-the-money options as being options on volatility. Why do you think they do this?
19.11. Suppose that a central bank’s policy is to allow an exchange rate to fluctuate between 0.97 and 1.03. What pattern of implied volatilities for options on the exchange rate would you expect
19.10. What problems do you think would be encountered in testing a stock option pricing model empirically?
19.9. What volatility smile is likely to be observed for six-month options when the volatility is uncertain and positively correlated to the stock price?
19.8. A stock price is currently $20. Tomorrow, news is expected to be announced that will either increase the price by $5 or decrease the price by $5. What are the problems in using
19.7. Explain what is meant by crashophobia.
19.5. Explain carefully why a distribution with a heavier left tail and less heavy right tail than the lognormal distribution gives rise to a downward sloping volatility smile.
19.3. What volatility smile is likely to be caused by jumps in the underlying asset price? Is the pattern likely to be more pronounced for a two-year rather than a three-month option?
19.2. What volatility smile is observed for equities?
18.21. How much is gained from exercising early at the lowest node at the nine-month point in Example 18.2?
18.20. Estimate delta, gamma, and theta from the tree in Example 18.1. Explain how each can be interpreted.
18.18. A six-month American call option on a stock is expected to pay dividends of $1 per share at the end of the second month and the fifth month. The current stock price is $30, the exercise price

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