Suppose the continuously compounded, risk-free interest rate is 3.75%, an investor creates a bull spread on a stock by purchasing a two-month European call option with a strike price of $100 for $7.57 and selling a two-month European call option with a strike price of $110 for $4.75. Find the profit to the investor if at expiry the stock is worth (a) $98, (b) $107, (c) $115. Suppose the continuously compounded, risk-free interest rate is 4.25%, an investor creates a bear spread on a stock by purchasing a three- month European put option with a strike price of $425 for $15.75 and selling a three-month European put option with a strike price of $400 for $10.25. Find the profit to the investor if at expiry the stock is worth (a) $375, (b) $410, (c) $450.

Suppose the continuously compounded, risk-free interest rate is 3.75%, an investor creates a bull spread on a stock by purchasing a two-month European call option with a strike price of $100 for $7.57 and selling a two-month European call option with a strike price of $110 for $4.75. Find the profit to the investor if at expiry the stock is worth (a) $98, (b) $107, (c) $115. Suppose the continuously compounded, risk-free interest rate is 4.25%, an investor creates a bear spread on a stock by purchasing a three- month European put option with a strike price of $425 for $15.75 and selling a three-month European put option with a strike price of $400 for $10.25. Find the profit to the investor if at expiry the stock is worth (a) $375, (b) $410, (c) $450.

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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A stock has a current price of $67. An option on this stock that expires in six months has an exercise price of $65. The stock will pay a dividend of $5 in three months. Assume an annualized volatility of 30% and a continuously compounded risk - free rate of 5% per annum. Use the Black - Sholes - Merton model to price this option. 1) Suppose the option is a European put. Calculate the value of the put. 2) Suppose this option is an American call. Use Black's approximation to calculate the value of this call.
Suppose XYZ stock pays no dividends and has a current price of $50. The forward price for delivery in 1 year is $55. Suppose the 1-year eective annual interest rate is 10%. (a) Graph the payo and prot diagrams for a forward contract on XYZ stock with a forward price of $55. (b) Is there any advantage to investing in the stock or the forward contract? Why? (c) Suppose XYZ paid a dividend of $2 per year and everything else stayed the same. Now is there any advantage to investing in the stock or the forward contract? Why?
Consider a European put and a European call option which are both written on a non-dividend paying stock, have the same strike price K = £80 and expire in T = 2 months. These options are trading for p = £21 and c = £30.80, respectively. The underlying stock price is S0 = £90. The continuously compounded risk-free rate of interest is r = 10% per annum. What is the present value of the arbitrage profit? Please explain your answer and show your workings. In your response, please show all cash flows (both today and at expiration) and explain why this is an arbitrage (i.e. risk-less) profit.
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 to maturity is 6 months. (a) Calculate u, d, and p for a two-step tree. (b) Value the option using a two-step tree.
Consider an American call and an American put with the same underlying stock share S paying no dividend, the same strike price K = $30 and the same expiration date T = 3 (months). Suppose that the stock price is $31, the risk-free interest rate is 10% per annum compounded continuously, the price of the American call option is $3, and the price of the American put option is $1. Using the no-arbitrage principle, prove that there exists an arbitrage opportunity then.
uppose an American put is trading for $16.50and an American call is trading for $15, whereboth options have identical terms. The underlying stock price is $99, and the exercise price is$100. The annual risk - free interest rate is 5 per cent, and the time to expiration for both optionsis one year. Assuming that the stock pays no dividends, identify the appropriate arbitrage trading strategy
Consider a European call option on a non-dividend-paying stock where the stock price is $33, the strike price is $36, the risk-free rate is 6% per annum, the volatility is 25% per annum and the time to maturity is 6 months. (a) Calculate u and d for a one-step binomial tree. (b) Value the option using a non arbitrage argument. (c) Assume that the option is a put instead of a call. Value the option using the risk neutral approach. (d) Verify that the European call and European put prices found in (b) and (c) satisfy the put-call parity.
A European call that will expire in one year is currently trading for $3. Assume the risk-free rate (based on continuous compounding) is 5%, the underlying stock price is $60 and the strike price is $55. a. Is there an arbitrage opportunity? b. Describe exactly what a trader should do to take advantage of the arbitrage opportunity assuming it exists. c. Determine the present value of the profit that the trader can earn assuming you identify an arbitrage opportunity. Use at least four decimal places for those questions that require a numerical answer.
3) Suppose that the price of a non-dividend-paying stock is $27, its vo itility is 20%, and the risk- free rate for all maturities is 6% per annum. Provide a table showing the relationship between profit and final stock price for a butterfly spread using European put option with strike prices of $20, $25, and $30 and a maturity of one year. Ignore the impact of time a e of money.
An institutional investor holds several European call options on a non-dividend-paying stock with a strike of $55. The current stock price is $65, while the continuously compounded risk-free rate is 2% p.a and volatility is 25%. Assuming that the market follows the assumptions of the Black-Scholes option model: (i) Calculate the price of a one-year call option on the stock. (ii) Calculate the price of a one-year put on the same stock with the same strike price.
A stock is selling today for $110. The stock has an annual volatility of 64 percent and the annual risk-free rate is 7 percent. c. Calculate the fair price for a 1 year European put option with an exercise price of $95. d. Calculate how much the current stock price would need to change for the purchaser of the put option to break even in one year. e. Calculate the level of volatility that would make a $95 call option sell for $30. (Use Goal Seek or Solver). f. Calculate the level of volatility that would make a $95 put option sell for $8. (Use Goal Seek or Solver). Please show work using excel
If a particular stock does not pay dividends and is currently priced at $24 per share, what should be the price of a call option with a maturity of one year and a strike price of $24.5 if put options with the same features currently cost $2? Assume a risk-free rate of 2%. (use 5 decimal places)

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