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options futures and other derivatives

Questions and Answers of Options Futures And Other Derivatives

When is it appropriate for an investor to purchase a butterfly spread?AppendixLO1
Call options on a stock are available with strike prices of $15, $171, and $20, and expiration dates in 3 months. Their prices are $4, $2, and $1, respectively. Explain how the options can be used to
What trading strategy creates a reverse calendar spread?AppendixLO1
What is the difference between a strangle and a straddle?AppendixLO1
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
Use put-call parity to relate the initial investment for a bull spread created using calls to the initial investment for a bull spread created using puts.AppendixLO1
Explain how an aggressive bear spread can be created using put options.AppendixLO1
Suppose that put options on a stock with strike prices $30 and $35 cost $4 and $7, respectively. How can the options be used to create (a) a bull spread and (b) a bear spread? Construct a table that
Use put-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.AppendixLO1
A call with a strike price of $60 costs $6. A put 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
Construct a table showing the payoff from a bull spread when puts with strike prices K and K2, with K > K, are used.AppendixLO1
An investor believes that there will be a big jump in a stock price, but is uncertain as to the direction. Identify six different strategies the investor can follow and explain the differences among
How can a forward contract on a stock with a particular delivery price and delivery date be created from options?AppendixLO1
"A box spread comprises four options. Two can be combined to create a long forward position and two can be combined to create a short forward position." Explain this statement.AppendixLO1
What is the result if the strike price of the put is higher than the strike price of the call in a strangle?AppendixLO1
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, $0.65, and $0.70. The risk-free interest rates in the
Three put options on a stock have the same expiration date and strike prices of $55, $60, and $65. The market prices are $3, $5, and $8, respectively. Explain how a butterfly spread can be created.
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 T > T. Draw a diagram showing the profit when
Draw a diagram showing the variation of an investor's profit and loss with the terminal stock price for a portfolio consisting of: (a) One share and a short position in one call option (b) Two shares
Suppose that the price of a non-dividend-paying stock is $32, its volatility is 30%, and the risk-free rate for all maturities is 5% per annum. Use Deriva Gem to calculate the cost of setting up the
A stock price is currently $40. It is known that at the end of 1 month it will be either $42 or $38. The risk-free interest rate is 8% per annum with continuous compounding. What is the value of a
Explain the no-arbitrage and risk-neutral valuation approaches to valuing a European option using a one-step binomial tree.AppendixLO1
What is meant by the "delta" of a stock option?AppendixLO1
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-free interest rate is 10% per annum with continuous compounding. What is the value of a
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
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 put prices satisfy put-call
What are the formulas for u and d in terms of volatility?AppendixLO1
Consider the situation in which stock price movements during the life of a European option are governed by a two-step binomial tree. Explain why it is not possible to set up a position in the stock
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
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 $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 $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
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 $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 ST is the stock
Calculate u,d, and p when a binomial tree is constructed to value an 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 $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
A stock price is currently $40. Over each 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)
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.AppendixLO1
A stock price is currently $30. During each 2-month period for the next 4 months it will increase by 8% or reduce by 10%. The risk-free interest rate is 5%. Use a two-step tree to calculate the value
Consider a European call option on a non-dividend-paying stock where 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 time
Repeat Problem 11.20 for an American put option on a futures contract. The strike price and the futures price are $50, the risk-free rate is 10%, the time to maturity is 6 months, and the volatility
Footnote 1 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 is a put rather
What would it mean to assert that the temperature at a certain place follows a Markov process? Do you think that temperatures do, in fact, follow a Markov process?AppendixLO1
Can a trading rule based on the past history of a stock's price ever produce returns that are consistently above average? Discuss.AppendixLO1
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
Variables X1 and X2 follow generalized Wiener processes, with drift rates and and variances of and o. What process does X + X2 follow if: (a) The changes in X, and X2 in any short interval of time
Consider a variable S that follows the process dS = dt + dz.For the first three years, =2 and = 3; for the next three years, =3 and = 4. If the initial value of the variable is 5, what is the
Suppose that G is a function of a stock price S and time. Suppose that s and are the volatilities of S and G. Show that, when the expected return of S increases by os, the growth rate of G increases
Stock A and stock B both follow geometric Brownian motion. Changes in any short interval of time are uncorrelated with each other. Does the value of a portfolio consisting of one of stock A and one
The process for the stock price in equation (12.8) is AS=S At+oSeAt where and or are constant. Explain carefully the difference between this model and each of the following: = + ASUS At+eAt = + Why
It has been suggested that the short-term interest rate follows the stochastic process dra(br) dt +redz wherea, b, c are positive constants and dz is a Wiener process. Describe the nature of this
Suppose that a stock price S follows geometric Brownian motion with expected return and volatility : dS=Sdt +Sdz What is the process followed by the variable S"? Show that S" also follows geometric
Suppose that x 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 dx = a(x-x) dt + sx dz wherea, xo, and s are
Suppose that a stock price has an expected return of 16% per annum and a volatility of 30% per annum. When the stock price at the end of a certain day is $50, calculate the following: (a) The
A company's cash position, measured in millions of dollars, follows a generalized Wiener process 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 x is the yield on a perpetual government bond that pays interest at the rate of $1 per annum. Assume that x is expressed with continuous compounding, that interest is paid continuously
If S follows the geometric Brownian motion process in equation (12.6), what is the process followed by (a) y = 2S (b) y= s (c) y = es (d) y = (-)/S In each case express the coefficients of dt and dz
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? (Hint: ST > 80 when
What does the Black-Scholes stock option pricing model assume about the probability distribution of the stock price in one year? What does it assume about the continuously compounded rate of return
The volatility of a stock price is 30% per annum. What is the standard deviation of the percentage price change in one trading day?AppendixLO1
Explain the principle of risk-neutral valuation.AppendixLO1
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
What difference does it make to your calculations in Problem 13.4 if a dividend of $1.50 is expected in 2 months?AppendixLO1
What is implied volatility? How can it be calculated?AppendixLO1
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 return (with continuous
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
Using the notation in this chapter, prove that a 95% confidence interval for ST is between Spe(-0/2)T-1.960-T and Spe/2)+1.960T AppendixLO1
A portfolio manager announces that the average of the returns realized in each year of the last 10 years is 20% per annum. In what respect is this statement misleading?AppendixLO1
Assume that a non-dividend-paying stock has an expected return of and a volatility of . An innovative financial institution has just announced that it will trade a security that pays off a dollar
Consider a derivative that pays off S at time T, where S7 is the stock price at that time. When the stock price follows geometric Brownian motion, it can be shown that its price at time t (t)where S
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%
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
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 $65, and the volatility
A call option on a non-dividend-paying stock has a market price of $21. 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
With the notation used in this chapter: (a) What is N'(x)?d = (b) Show that SN'(d) = Ke'(-)N'(d), where S is the stock price at time t and In(S/K)+(+02/2)(T-t) oT-1 In(S/K)+(-2/2)(T-t) d = oT-t (c)
Show that the Black-Scholes formulas for call and put options satisfy put-call parity.AppendixLO1
A stock price is currently $50 and the risk-free interest rate is 5%. Use the DerivaGem software to translate the following table of European call options on the stock into a table of implied
Explain carefully why Black's approach to evaluating an American call option on a dividend-paying stock may give an approximate answer even when only one dividend is anticipated. Does the answer
Consider an American call option on a stock. The stock price is $50, the time to maturity is 15 months, the risk-free rate of interest is 8% per annum, the exercise price is $55, and the volatility
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, N(d2). What is an expression for the value of a
Show that S-2/2 could be the price of a traded security.AppendixLO1
A company has an issue of executive stock options outstanding. Should dilution be taken into account when the options are valued? Explain your answer.AppendixLO1
A company's stock price is $50 and 10 million shares are outstanding. The company is considering giving its employees 3 million at-the-money 5-year call options. Option exercises will be handled by
A stock price is currently $50. Assume that the expected return from the stock is 18% and its volatility is 30%. What is the probability distribution for the stock price in 2 years? Calculate the
Suppose that observations on a stock price (in dollars) at the end of each of 15 consecutive weeks are as follows: 30.2, 32.0, 31.1, 30.1, 30.2, 30.3, 30.6, 33.0, 32.9, 33.0, 33.5, 33.5, 33.7, 33.5,
A financial institution plans to offer a security that pays off a dollar amount equal to s at time T. (a) Use risk-neutral valuation to calculate the price of the security at time t in terms of the
Consider an option on a non-dividend-paying stock when the stock price is $30, the exercise price is $29, the risk-free interest rate is 5%, the volatility is 25% per annum, and the time to maturity
Assume that the stock in Problem 13.29 is due to go ex-dividend in 1 months. The expected dividend is 50 cents. (a) What is the price of the option if it is a European call? (b) What is the price of
Consider an American call option when the stock price is $18, the exercise price is $20, the time to maturity is 6 months, the volatility is 30% per annum, and the risk-free interest rate is 10% per
A portfolio is currently worth $10 million and has a beta of 1.0. The S&P 100 is currently standing at 500. Explain how a put option on the S&P 100 with a strike of 480 can be used to provide
"Once we know how to value options on a stock paying a dividend yield, we know how to value options on stock indices, currencies, and futures." Explain this statement.AppendixLO1
A stock index is currently 300, the dividend yield on the index is 3% per annum, and the risk-free interest rate is 8% per annum. What is a lower bound for the price of a 6-month European call option
A currency is currently worth $0.80. Over each of the next 2 months it is expected to increase or decrease in value by 2%. The domestic and foreign risk-free interest rates are 6% and 8%,
Explain the difference between a call option on yen and a call option on yen futures.AppendixLO1
Explain how currency options can be used for hedging.AppendixLO1
Calculate the value of a 3-month at-the-money European call option on a stock index when the index is at 250, the risk-free interest rate is 10% per annum, the volatility of the index is 18% per
Consider an American call futures option where the futures contract and the option contract expire at the same time. Under what circumstances is the futures option worth more than the corresponding
Calculate the value of an 8-month European put option on a currency with a strike price of 0.50. The current exchange rate is 0.52, the volatility of the exchange rate is 12%, the domestic risk-free
Why are options on bond futures more actively traded than options on bonds?AppendixLO1
"A futures price is like a stock paying a dividend yield." What is the dividend yield?AppendixLO1

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