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business
options futures and other derivatives

Questions and Answers of Options Futures And Other Derivatives

A company has an issue of executive stock options outstanding. Should dilution be taken into account when the options are valued? Explain your answer.
Show that could be the price of a traded security.
Show that the probability that a European call option will be exercised in a risk-neutral world is, with the notation introduced in this chapter, Nid). What is an expression for the value of a
Consider an American call option on a stock. The stock price is $50, the time to maturity 15 months, the risk-free rate of interest is 8% per annum, the exercise price is $55, and the volatility in
A stock price is currently $50 and the risk-free interest rate is 5%. Use the DerivaG software to translate the following table of European call options on the stock into a table of implied
With the notation used in this chapter: (a) What is ( (b) Show that SN (d) = Ked), where S in the stock price at time and In[5/K)+(y+0/2XT-1) (c) Calculate id,/as and id/as. (d) Show that when it
A call option on a non-dividend-paying stock has a market price of $2 The stock price is $15, the exercise price is $13, the time to maturity is 3 months, and the risk-free interest rate is 5% per
Consider an American call option on a stock. The stock price is $70, the time to maturity is 8 months, the risk-free rate of interest is 10% per annum, the exercise price is $5, and the volatility is
What is the price of a European put option on a non-dividend-paying stock when the stock price is $69, the strike price is $70, the risk-free interest rate is 5% per annum, the volatility is 35% per
What is the price of a European call option on a non-dividend-paying stock when the stock price is $52, the strike price is $50, the risk-free interest rate is 12% per annum, the volatility is 30%
Consider a derivative that pays off at time T, where Sy is the stock price at that time. When the stock price follows geometric Brownian motion, it can be shown that is price at time (7) has the form
Assume that a non-dividend-paying stock has an expected return of a and a volatility of o. An innovative financial institution has just announced that it will trade a security that pays off a dollar
Using the notation in this chapter, prove that a 95% confidence interval for Sy is betwee
A stock price follows geometric Brownian motion with an expected return of 16% and a volatility of 35%. The current price is $38. (a) What is the probability that a European call option on the stock
A stock price is currently $40. Assume that the expected return from the stock is 15% and that its volatility is 25%. What is the probability distribution for the rate of retur (with continuous
What difference does it make to your calculations in Problem 13.4 if a dividend of $1.50 is expected in 2 months?
Calculate the price of a 3-month European put option on a non-dividend paying stock with a strike price of $50 when the current stock price is $50, the risk-free interest rate is 10% per annum, and
A stock price is currently 50. Its expected return and volatility are 12% and 30%, respectively. What is the probability that the stock price will be greater than 80 in 2 years? (H: S>80 when In Sp>
If 3 follows the geometric Brownian motion process in equation (12.6), what is the process followed by (B)=25 (b) y= (y= (d) In each case express the coefficients of dr and dz in terms of y rather
A company's cash position, massured in millions of dollars, follows a generalized Wiener pros with a drift rate of 0.1 per month and a variance rate of 0.16 per month. The initial cash position is
Suppose that is the yield to maturity with continuous compounding on a zero-coupon bond that pays off $1 at time 7. Assume that x follows the process dr=x-x)+x where x, and are positive constants and
Suppose that a stock price S follows geometric Brownian motion with expected return and volatility a -+ What is the process followed by the variable Show that S also follows geometric Brownian motion.
It has been suggested that the short-term interest rate r follows the stochastic process = (-)+red wherea, b, c are positive constants and dr is a Wimer process, Describe the nature of this process
The process for the stock price in equation (12.8) is where and are constant. Explain carefully the difference between this model and each of the following: AS-SA+I Way is the model in equation (123)
Suppose that is a function of a stock price S and time. Suppose that ex und do are the volatilities of S and G. Show that, when the expected reture of S increases by, the growth rate of G increases
Consider a variable S that follows the process + For the first three years, 2 and 3; for the next three years, -3 and -4. Ir the initial value of the variable is 5, what is the probability
Variables X and X, follow generalized Wiener processes, with drift rates, and pand variances of and What process does X, +X, follow if (a) The changes in X, and X, in any shoet interval of time are
A company's cash position, measured in millions of dollars, follows a generalized Wiener process with a drift rate of 0.5 per quarter and a variance rate of 4.0 per quarter. How high does the
What would it move to avert that the temperature at a certain place follows a Marko proces? Do you think that temperatures do, in fact, follow a Markov process!
Footnote shows that the correct discount rate to use for the real-world expected payoff in the case of the call option considered in Figure 11.1 is 42.6%. Show that if the option saput rather than a
Consider a European call option on a non-dividend paying stock witere the stock price is $40, the strike price is $40, the risk-free rate is 4% per annum, the volatility is 30% per annum, and the
Using a "trial-and-error" approach, estimate how high the strike price has to be in Problem 11.17 for it to be optimal to exercise the option immediately. 11.19: A stock price is currently $30.
A stock price is currently $40. Over much of the next two 3-month periods it is expected to go up by 10% or down by 10%. The risk-free interest rate is 12% per annum with continuous compounding (a)
A stock price is currently $50. It is known that at the end of 6 months it will be either $60 or $42. The risk-free rate of interest with continuous compounding is 12% per annum. Calculate the value
Calculateu,d, and p when a binomial tree is constructed to value at option on a foreign currency. The tree step size is 1 month, the domestic interest rate is 5% per annum, the foreign interest rate
A stock price is currently $25. It is known that at the end of 2 months it will be either $23 or $27. The risk-free interest rate is 10% per annum with continuous compounding Suppose Sr is the stock
For the situation considered in Problem 11.12, what is the value of a 6-month European put option with a strike price of $51? Verify that the European call and European put prices satisfy put-call
A stock price is currently $50. Over each of the next two 3-month periods it is expected to go up by 6% or down by 5%. The risk-free interest rate is 5% per annum with continuous compounding. What is
A stock price is currently $40. It is known that at the end of 3 months it will be either $45 or $35. The risk-free rate of interest with quarterly compounding is 8% per annum. Calculate the value of
A stock price is currently $80. It is known that at the end of 4 months it will be either $75 or $85. The risk-free interest rate is 5% per annum with continuous compounding. What is the value of a
A stock price is currently $50. It is known that at the end of 2 months it will be either $53 or $48. The risk-free interest rate is 10% per annum with continuous compounding. What is the value of a
Consider the situation in which stock price movements during the life of a European option are governed by a two-step binomial tras Explain why it is not possible to set up a position in the stock
What are the formules for u and d in terms of volatility?
For the situation considered in Problem 11.5, what is the value of a 1-year European put option with a strike price of $100? Verify that the European call and European pat prices satisfy put-call
A stock price is currently $100. Over each of the next two 6-month periods it is expected to go up by 10% or down by 10%. The risk-free interest rate is 8% per annum with continuous compounding, What
A stock price is currently $50. It is known that at the end of 6 months it will be either $45 or $55. The risk tree interest rate is 10% per annum with continuous compounding. What is the value of a
A stock price is currently 540. It is known that at the end of 1 month it will be either 542 or $38. The risk free interest rate is 8% per annum with continuous compounding What is the value of a
A diagonal spread is created by buying a call with strike price K, and exercise date T and selling a call with strike price K, and exercise date T,, where 7> > 7. Draw a diagram showing the profit
One Australian dollar is currently worth $0.64. A 1-year butterfly spread is set up using European call options with strike prices of $0.60, 30.65, and $0.70. The risk-free interest cates in the
What is the result if the strike price of the pet is higher than the strike price of the callin a strangle?
Construct a table showing the payoff from a bull spread when puts with strike prices K and Ky, with K; > K, are used. 10:14. An investor believes that there will be a big jump in a stock price, but
A call with a strike price of 560 costs $6. A pet with the same strike price and expiration date costs $4. Construct a table that shows the profit from a straddle. For what range of stock prices
Lepat-call parity to show that the cost of a butterfly spread created from European puts is identical to the cost of a butterfly spread created from European calls.
Suppose that put options on a stock with strike price $30 and $35 cost $4 and $7, respectively. How can the options be used to create (a) a ball spread and (b) a bear spread? Construct a table that
A call option with a strike price of $50 costs $2. A put option with a strike price of $45 costs $3. Explain how a strangle can be created from these two options. What is the pattern of profits from
Call options on a stock are available with strike prices of S15, $171, and $20, and expiration dates in 3 months. Their prices are 54, 52, and Sj, respectively. Explain how the options can be used to
What is meant by a protective put? What position in call options is equivalent to a protective pur
What is the result corresponding to that in Problem 9.23 for European put options? 9.15.Suppose that you are the manager and sole owner of a highly leveraged company. All the debt will mature in 1
Suppose that es, and cy are the prices of European call options with strike prices K. K., and Ks, respectively, where K, K K and Ks-K-K-K. All options have the same maturity. Show that
A European call option and put option on a stock both have a strike price of $20 and an expiration date in 3 months. Both sell for $3. The risk-free interest rate is 10% per annum. the current stock
Use the software DerivaGem to verify that Figures 9.1 and 9.2 are correct
Regular call options on non-dividend-paying stocks should not be exercised early. How- ever, there is a tendency for executive stock options to be exercised early even when the company pays no
Prove the result in equation (98) (fur For the first part of the relationship, consider (a) a portfolio consisting of a European call plus an amount of cash equal to D+K, and (b) a portfolio
Prove the mult in equation (9.4) (Hau: For the first part of the relationship, consider (a) a portfolio consisting of a European call plus an amount of cash equal to K, and (b) a portfolio consisting
Explain carefully the arbitrage opportunities in Problem 9.16 if the American put price is greater than the calculated upper bound.
The price of an American call on a non-dividend-paying stock is $4. The stock price is $31, the strike price is $30, and the expiration date is in 3 months. The risk-free interest rate is 8%. Derive
Explain carefully the arbitrage opportunities in Problem 9.14 if the European put price
Give an intuitive explanation of why the early exercise of an American put becomes more attractive as the risk-free rate increases and volatility decreases 9.14 The price of a European call that
A 1-month European put option on a non-dividend paying stock is currently selling for $2.30. The stock price is $47, the strike price is $50, and the risk-free interest rate is 6% per annum. What
A 4-month European call option on a dividend paying stock is currently selling for $5. The stock price is $64, the strike price is $60, and a dividend of $0.30 is expected in I month. The risk-free
What is a lower bound for the price of a 2-month European put option on a non- dividend paying stock when the stock price is $58, the strike price is $65, and the risk-free interest rate is 5% per
What is a lower bound for the price of a 6-month call option on a non-dividend paying stock when the stock price is $80, the strike price is $75, and the risk-free interest rate is 10% per annum
Explain why the arguments leading to put-call parity for European options cannot be used to give a similar sesalt for American options
The price of a non-dividend paying stock is $19 and the price of a 3-month European call option on the stock with a strike price of $20 is $1. The risk-free rate is 4% per annum. What is the price of
Explain why an American call option on a dividend-paying stock is always worth at least as much as its intrinsic value. Es the same true of a European call option? Explain your
What is a lower bound for the price of a 1-month European put option on a non- dividend-paying stock when the stock price is $12, the strike price is $15, and the risk-free interest rate is 6% per
What is a lower bound for the price of a 4-month call option on a non-dividend-paying stock when the stock price is $28, the strike price is $25, and the risk-free interest rate is 8% per annum?
List the six factors that affect stock option prices.
On July 20, 2004, Microsoft surprised the market by announcing a $3 dividend. The ex- dividend date was November 17, 2004, and the payment date was December 2, 2004. Its stock price at the time was
The price of a stock is $40. The price of a 1-year European put option on the stock with a strike price of $30 is quoted as $7 and the price of a 1-year European call option on the stock with a
A United States investor writes five naked call option contracts. The option price $3.50, the strike price is $60.00, and the stock price is $57.00. What is the initial margin requirement?
Options on General Motors stock are on a March, June, September, and December cycle What options trade on (a) March 1, (b) June 30, and (c) August S?
What is the effect of an unexpected cash dividend on (a) a call option price and (b) a pat uption price?
Consider an exchange-traded call option contract to buy 500 shares with a strike price of 540 and maturity is 4 months. Explain how the terms of the option contract change whe there is: (a) a 10%
The treasurer of a corporation is trying to choose between options and forward contracts to hodge the corporation's foreign exchange risk. Discuss the advantages and disadvantages of each.
Explain why an American option is always worth at least as much as its intrinsic value. 8:15. Explain carefully the difference between writing a put option and buying a call option.
Suppose that a European pat option to sell a share for $60 costs $8 and is held until maturity. Under what circumstances will the seller of the option (the party with the short position) make a
Suppose that a European call option to buy a share for $100.00 costs $5.00 and is held until maturity. Under what circumstances will the holder of the option make a profic? Under what circumstances
A corporate treasurer is designing a hedging program involving foreign currency options. What are the pros and cons of waing (a) the Philadelphia Stock Exchange and (b) the over-the-counter market
How is an executive stock option different from a regular exchange-traded or over-the- counter American-style stock option?
A company declares a 2-for-1 stock spitt. Explain how the terms change for a call option with a strike price of $60.
A stock option is on a February, May, August, and November cycle. What options trade on (a) April I and (b) May 30
An investor sells a European call on a share for $4. The stock price is $47 and the strike price is $50. Under what circumstances does the investor make a profit? Under what circumstances will the
An investor buys a European put on a share for $3. The stock price is $42 and the strike price is $40. Under what circumstances does the investor make a profit? Under what circumstances will the
Company X is based in the United Kingdom and would like to borrow $50 million at a fixed rate of interest for 5 years in US funds Because the company is not well known in the United States, this has
Under the terms of an interest rate swap, a financial institution has agreed to pay 10% per annum and to receive 3-month LIBOR in retum on a notional principal of $100 million with payments being
Company A, a British manufacturer, wishes to borrow US dollars at a fixed rate of Interest. Company B, a US multinational, wishes to borrow sterling at a fixed rate of interest. They have been quoted
The 1-year LIBOR rate is 10%. A bank trades swaps where a fixed rate of interest is exchanged for 12 month LIBOR with payments being exchanged annually. The 2- and 3-year swap rates (expressed with
Why is the expected loss from a default on a swap less than the expected loss from the default on a loan with the same principal? 7.16, A bank finds that its assets are not matched with its
After it hedges les foreign exchange risk using forward contracts, is the Snancial institution's average spread in Figure 7.10 likely to be greater than or less than 20 basis points? Explain your

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