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options futures and other derivatives

Questions and Answers of Options Futures And Other Derivatives

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,
When there are two barriers how can a tree be designed so that nodes lie on both barriers? Lop58
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 26.8. 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 26.4 is correct. Lop58
Can the approach for valuing path-dependent options in Section 26.5 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? Lop58
Use a three-time-step tree to value an American floating 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
"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 why. Lop58
"The IVF model does not necessarily get the evolution of the volatility surface correct." Explain this statement. Lop58
Write down the equations for simulating the path followed by the asset price in the stochastic volatility model in equations (26.2) and (26.3). Lop58
At time 0 the price of a non-dividend-paying stock is So. Suppose that the time interval between 0 and T is divided into two subintervals of length t, and t. During the first subinterval, the
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-Merton to
Confirm that Merton's jump-diffusion model satisfies put-call parity when the jump size is lognormal. Lop58
Use Monte Carlo simulation to show that Merton's value for a European option is correct when r = 0.05, q=0,= 0.3, k = 0.5, 0.25, and So = 30. Lop58
Confirm that the CEV model formulas satisfy put-call parity. Lop58
Produce a formula for valuing a cliquet option where an amount Q is invested to produce a payoff at the end of n periods. The return earned each period is the greater of the return on an index
What is the relationship between a regular call option, a binary call option, and a gap call option? Lop58
Carry out the analysis in Example 25.4 of Section 25.15 to value the variance swap on the assumption that the life of the swap is 1 month rather than 3 months. Lop58
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 company's stock.
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 18.2 and 18.3 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 the appendix 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 25.15. 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 %,? Lop58
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.
Value the variance swap in Example 25.4 of Section 25.15 assuming that the implied volatilities for options with strike prices 800, 850, 900, 950, 1,000, 1,050, 1,100, 1,150, 1,200 are 20%, 20.5%,
Explain adjustments that have to be made when r --: q for (a) the valuation formulas for floating lookback call options in Section 25.10 and (b) the formulas for M1 and M2 in Section 25.12.
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 floating 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
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? Lop58
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 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? Lop58
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
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, Lop58
Explain why delta hedging is easier for Asian options than for regular options. Lop58
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? Lop58
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. Lop58
Section 25.8 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 T2 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 floating lookback call and a floating lookback put with the same maturity. Lop58
Explain the difference between a forward start option and a chooser option. Lop58
Table 24.6 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. Assume
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
In Example 24.2, what is the tranche spread for the 6% to 9% tranche? Lop58
In Example 24.3, what is the spread for (a) a first-to-default CDS and (b) a second-to default CDS? Lop58
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 returns offered on the various tranches in a synthetic CDO to change when the correlation between the bonds in the portfolio increases. Lop58
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
In Example 24.2, what is the tranche spread for the 9% to 12% tranche? Lop58
Explain the difference between base correlation and compound correlation. Lop58
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,
What is the difference between a total return swap and an asset swap? Lop58
Does valuing a CDS using real-world default probabilities rather than risk-neutral default probabilities overstate or understate its value? Explain your answer. Lop58
Why is there a potential asymmetric information problem in credit default swaps? Lop58
"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. Lop58
Explain how forward contracts and options on credit default swaps are structured. Lop58
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 24.1 to 24.4 is 100 basis points, 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. Lop58
What is the formula relating the payoff on a CDS to the notional principal and the recovery rate? Lop58
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 24.8 if it is a binary CDS? Lop58
What is the value of the swap in Problem 24.8 per dollar of notional principal to the protection buyer if the credit default swap spread is 150 basis points? Lop58
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. Lop58
Explain the difference between risk-neutral and real-world default probabilities. Lop58
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. Lop58
Explain how a cash CDO and a synthetic CDO are created. Lop58
Explain the two ways a credit default swap can be settled. Lop58
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 default occurs after 4
Explain the difference between a regular credit default swap and a binary credit default swap. Lop58
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
Give an example of (a) right-way risk and (b) wrong-way risk. Lop58
Suppose that the spread between the yield on a 3-year zero-coupon riskless bond and a 3-year zero-coupon bond issued by a corporation is 1%. By how much does Black- Scholes-Merton overstate the value
Show that under Merton's model in Section 23.6 the credit spread on a T-year zero- coupon bond is - In[N(d2) + N(-d)/L]/T, where L = De/Vo? Lop58
Suppose that in an asset swap B is the market price of the bond per dollar of principal, B is the default-free value of the bond per dollar of principal, and V is the present value of the asset swap
Does put-call parity hold when there is default risk? Explain your answer. Lop58
"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. Lop58
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. Lop58
Explain why the credit exposure on a matched pair of forward contracts resembles a straddle. Lop58
"A long forward contract subject to credit risk is a combination of a short position in a no-default put and a long position in a call subject to credit risk." Explain this statement. Lop58
Suppose that in Problem 23.15, the 6-month forward rate is also 1.50 and the 6-month dollar risk-free interest rate is 5% per annum. Suppose further that the 6-month dollar rate of interest at which
A company enters into a 1-year forward contract to sell $100 for AUD150. The contract is initially at the money. In other words, the forward exchange rate is 1.50. The 1-year dollar risk-free rate of
Suppose that a financial institution has entered into a swap dependent on the sterling interest rate with counterparty X and an exactly offsetting swap with counterparty Y. Which of the following
A company has issued 3- and 5-year bonds with a coupon of 4% per annum payable annually. The yields on the bonds (expressed with continuous compounding) are 4.5% and 4.75%, respectively. Risk-free
A 4-year corporate bond provides a coupon of 4% per year payable semiannually and has a yield of 5% expressed with continuous compounding. The risk-free yield curve is flat at 3% with continuous

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