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options futures and other derivatives

Questions and Answers of Options Futures And Other Derivatives

An oil company is set up solely for the purpose of exploring for oil in a certain small area of Texas. Its value depends primarily on two stochastic variables: the price of oil and the quantity of
Consider two securities both of which are dependent on the same market variable. The expected returns from the securities are 8% and 12%. The volatility of the first security is 15%. The
Suppose that the market price of risk for gold is zero. If the storage costs are 1% per annum and the risk-free rate of interest is 6% per annum, what is the expected growth rate in the price of
How is the market price of risk defined for a variable that is not the price of an investment asset?AppendixLO1
Consider the situation in Merton's jump-diffusion model where the underlying asset is a non-dividend-paying stock. The average frequency of jumps is one per year. The average percentage jump size is
Repeat the analysis in Section 24.7 for the put option example on the assumption that the strike price is 1.13. Use both the least squares approach and the exercise boundary parameterization
Suppose that the volatilities used to price a 6-month currency option are as in Table 16.2. Assume that the domestic and foreign risk-free rates are 5% per annum and the current exchange rate is
A new European-style lookback call option on a stock index has a maturity of 9 months. The current level of the index is 400, the risk-free rate is 6% per annum, the dividend yield on the index is 4%
When there are two barriers how can a tree be designed so that nodes lie on both barriers?AppendixLO1
Consider a European put option on a non-dividend paying stock when the stock price is $100, the strike price is $110, the risk-free rate is 5% per annum, and the time to maturity is one year. Suppose
Examine the early exercise policy for the eight paths considered in the example in Section 24.7. What is the difference between the early exercise policy given by the least squares approach and the
Verify that the 6.492 number in Figure 24.3 is correct.AppendixLO1
Can the approach for valuing path-dependent options in Section 24.4 be used for a 2-year American-style option that provides a payoff equal to max(Save - K, 0), where Save is the average asset price
Use a three-time-step tree to value an American put option on the geometric average of the price of a non-dividend-paying stock when the stock price is $40, the strike price is $40, the risk-free
What happens to the variance-gamma model as the parameter tends to zero?AppendixLO1
Use a three-time-step tree to value an American lookback call option on a currency when the initial exchange rate is 1.6, the domestic risk-free rate is 5% per annum, the foreign risk-free interest
"When interest rates are constant the IVF model correctly values any derivative whose payoff depends on the value of the underlying asset at only one time." Explain this statement.AppendixLO1
"The IVF model does not necessarily get the evolution of the volatility surface correct." Explain this statement.AppendixLO1
Write down the equations for simulating the path followed by the asset price in the stochastic volatility model in equations (24.2) and (24.3).AppendixLO1
Consider the case of Merton's jump-diffusion model where jumps always reduce the asset price to zero. Assume that the average number of jumps per year is . Show that the price of a European call
Suppose that the volatility of an asset will be 20% from month 0 to month 6, 22% from month 6 to month 12, and 24% from month 12 to month 24. What volatility should be used in Black-Scholes to value
Confirm that Merton's jump-diffusion model satisfies put-call parity when the jump size is lognormal.AppendixLO1
Explain how you would use Monte Carlo simulation to sample paths for the asset price when Merton's jump-diffusion model is used.AppendixLO1
Confirm that the CEV model formulas satisfy put-call parity.AppendixLO1
An insurance company's losses of a particular type are to a reasonable approximation normally distributed with a mean of $150 million and a standard deviation of $50 million. (Assume no difference
Explain how a 5 x 8 option contract for May 2006 on electricity with daily exercise works. Explain how a 5 x 8 option contract for May 2006 on electricity with monthly exercise works. Which is worth
How can an energy producer use derivatives markets to hedge risks?AppendixLO1
What are the characteristics of an energy source where the price has a very high volatility and a very high rate of mean reversion? Give an example of such an energy source.AppendixLO1
Would you expect the volatility of the 1-year forward price of oil to be greater than or less than the volatility of the spot price? Explain your answer.AppendixLO1
Suppose that you have 50 years of temperature data at your disposal. Explain carefully the analyses you would carry out to value a forward contract on the cumulative CDD for a particular
"HDD and CDD can be regarded as payoffs from options on temperature." Explain this statement.AppendixLO1
Why is the historical data approach appropriate for pricing a weather derivatives contract and a CAT bond?AppendixLO1
Why is the price of electricity more volatile than that of other energy sources?AppendixLO1
Distinguish between the historical data and the risk-neutral approach to valuing a derivative. Under what circumstance do they give the same answer.AppendixLO1
How is a typical natural gas forward contract structured?AppendixLO1
What is meant by HDD and CDD?AppendixLO1
In the DerivaGem Application Builder Software modify Sample Application D to test the effectiveness of delta and gamma hedging for a call on call compound option on a 100,000 units of a foreign
Use the DerivaGem Application Builder software to compare the effectiveness of daily delta hedging for (a) the option considered in Tables 15.2 and 15.3 and (b) an average price call with the same
Suppose that a stock index is currently 900. The dividend yield is 2%, the risk-free rate is 5%, and the volatility is 40%. Use the results in Appendix 19A to calculate the value of a 1-year average
Consider a down-and-out call option on a foreign currency. The initial exchange rate is 0.90, the time to maturity is 2 years, the strike price is 1.00, the barrier is 0.80, the domestic risk-free
Sample Application F in the DerivaGem Application Builder Software considers the static options replication example in Section 22.13. It shows the way a hedge can be constructed using four options
Consider an up-and-out barrier call option on a non-dividend-paying stock when the stock price is 50, the strike price is 50, the volatility is 30%, the risk-free rate is 5%, the time to maturity is
What is the value in dollars of a derivative that pays off 10,000 in 1 year provided that the dollar/sterling exchange rate is greater than 1.5000 at that time? The current exchange rate is 1.4800.
Explain adjustments that has to be made when r = q for (a) the valuation formulas for lookback call options in Section 22.8 and (b) the formulas for M, and M, in Section 22.10.AppendixLO1
Use DerivaGem to calculate the value of: (a) A regular European call option on a non-dividend-paying stock where the stock price is $50, the strike price is $50, the risk-free rate is 5% per annum,
Estimate the value of a new 6-month European-style average price call option on a non- dividend-paying stock. The initial stock price is $30, the strike price is $30, the risk-free interest rate is
A new European-style lookback call option on a stock index has a maturity of 9 months. The current level of the index is 400, the risk-free rate is 6% per annum, the dividend yield on the index is 4%
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
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
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?AppendixLO1
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
Does a lookback call become more valuable or less valuable as we increase the frequency with which we observe the asset price in calculating the minimum?AppendixLO1
Answer the following questions about compound options: (a) What put-call parity relationship exists between the price of a European call on a call and a European put on a call? Show that the formulas
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?AppendixLO1
Calculate the price of a 1-year European option to give up 100 ounces of silver in exchange for I ounce of gold. The current prices of gold and silver are $380 and $4, respectively; the risk-free
Explain why delta hedging is easier for Asian options than for regular options.AppendixLO1
If a stock price follows geometric Brownian motion, what process does A(t) follow where A(t) is the arithmetic average stock price between time zero and time t?AppendixLO1
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
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 call
Explain why a down-and-out put is worth zero when the barrier is greater than the strike price.AppendixLO1
Section 22.6 gives two formulas for a down-and-out call. The first applies to the situation where the barrier, H, is less than or equal to the strike price, K. The second applies to the situation
The text derives a decomposition of a particular type of chooser option into a call maturing at time T, and a put maturing at time T. Derive an alternative decomposition into a call maturing at time
Suppose that c and p are the prices of a European average price call and a European average price put with strike price K and maturity T,c, and p2 are the prices of a European average strike call and
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
Describe the payoff from a portfolio consisting of a lookback call and a lookback put with the same maturity.AppendixLO1
Explain the difference between a forward start option and a chooser option.AppendixLO1
A 3-year convertible bond with a face value of $100 has been issued by company ABC. It pays a coupon of $5 at the end of each year. It can be converted into ABC's equity at the end of the first year
Suppose that: (a) The yield on a 5-year risk-free bond is 7%. (b) The yield on a 5-year corporate bond issued by company X is 9.5%. (c) A 5-year credit default swap providing insurance against
Explain how you would expect the yields offered on the various tranches in a CDO to change when the correlation between the bonds in the portfolio increases.AppendixLO1
Assume that the default probability for a company in a year, conditional on no earlier defaults is and the recovery rate is R. The risk-free interest rate is 5% per annum. Default always occurs
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 years, 0.75 years, 1.25 years, and 1.75 years in a 2-year plain
What is a CDO squared? How about a CDO cubed?AppendixLO1
Suppose that in a one-factor Gaussian copula model the 5-year probability of default for each of 125 names is 3% and the pairwise copula correlation is 0.2. Calculate, for factor values of -2, -1, 0,
Consider an 18-month zero-coupon bond with a face value of $100 that can be converted into five shares of the company's stock at any time during its life. Suppose that the current share price is $20,
What is the difference between a total return swap and an asset swap?AppendixLO1
Does valuing a CDS using real-world default probabilities rather than risk-neutral default probabilities overstate or understate its value? Explain your answer.AppendixLO1
Explain how forward contracts and options on credit default swaps are structured.AppendixLO1
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% is
Verify that if the CDS spread for the example in Tables 21.1 to 21.4 is 100 basis points and the probability of default in a year (conditional on no earlier default) must be 1.61%. How does the
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.AppendixLO1
How is the recovery rate of a bond usually defined?AppendixLO1
How does a 5-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 default
What is the credit default swap spread in Problem 21.8 if it is a binary CDS?AppendixLO1
What is the value of the swap in Problem 21.8 per dollar of notional principal to the protection buyer if the credit default swap spread is 150 basis points?AppendixLO1
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 5-year credit default swap. Suppose that the
Explain why a total return swap can be useful as a financing tool.AppendixLO1
Explain the difference between risk-neutral and real-world probabilities.AppendixLO1
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.AppendixLO1
Explain how a CDO and a synthetic CDO are created.AppendixLO1
A credit default swap requires a semiannual payment at the rate of 60 basis points per year. The principal is $300 million and the credit default swap is settled in cash. A dfault occurs after 4
Explain the difference between a regular credit default swap and a binary credit default swap.AppendixLO1
Suppose that a bank has a total of $10 million of exposures of a certain type. The 1-year probability of default averages 1% and the recovery rate averages 40%. The copula correlation parameter is
The value of a company's equity is $4 million and the volatility of its equity is 60%. The debt that will have to be repaid in 2 years is $15 million. The risk-free interest rate is 6% per annum. Use
Explain carefully the distinction between real-world and risk-neutral default probabil- ities. Which is higher? A bank enters into a credit derivative where it agrees to pay $100 at the end of 1 year
A company has 1- and 2-year bonds outstanding, each providing a coupon of 8% per year payable annually. The yields on the bonds (expressed with continuous compound- ing) are 6.0% and 6.6%,
Suppose a 3-year corporate bond provides a coupon of 7% per year payable semiannu- ally and has a yield of 5% (expressed with semiannual compounding). The yields for all maturities on risk-free bonds
Show that under Merton's model in Section 20.6 the credit spread on a T-year zero- coupon bond is In[N(d) + N(-d)/L]/T, where L= DeT/Vo.AppendixLO1
Does put-call parity hold when there is default risk? Explain your answer.AppendixLO1
"When a bank is negotiating currency swaps, it should try to ensure that it is receiving the lower interest rate currency from a company with a low credit risk." Explain why.AppendixLO1
Explain why the impact of credit risk on a matched pair of interest rate swaps tends to be less than that on a matched pair of currency swaps.AppendixLO1

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