The stock price of Amazon is $50. The price of a 4-month European call option and a European put option on the stock with a strike price of $50 is $3. The stock pays $0.5 in dividends in one month and $0.75 in three months. The risk-free interest rate is flat at 4% per annum. Determine which of the following statements is true. OI. The put-call parity relationship holds so there are no arbitrage opportunities. O II. There are arbitrage opportunities given by sellig short the call option and borrowing $50 at the risk-free rate until maturity to buy the stock and the put option. O III. There are arbitrage opportunities given by sellig short the call option and borrowing $48.7591 at the risk-free rate until maturity to buy the stock and the put option. Note that 48.7591=50 - D, with D the present value of all dividend payments. O IV. There are arbitrage opportunities given by sellig short the stock and put option and buying the call option. The proceeds of this strategy, given by $50, are invested at the risk-free rate until maturity of the options.

The stock price of Amazon is $50. The price of a 4-month European call option and a European put option on the stock with a strike price of $50 is $3. The stock pays $0.5 in dividends in one month and $0.75 in three months. The risk-free interest rate is flat at 4% per annum. Determine which of the following statements is true. OI. The put-call parity relationship holds so there are no arbitrage opportunities. O II. There are arbitrage opportunities given by sellig short the call option and borrowing $50 at the risk-free rate until maturity to buy the stock and the put option. O III. There are arbitrage opportunities given by sellig short the call option and borrowing $48.7591 at the risk-free rate until maturity to buy the stock and the put option. Note that 48.7591=50 - D, with D the present value of all dividend payments. O IV. There are arbitrage opportunities given by sellig short the stock and put option and buying the call option. The proceeds of this strategy, given by $50, are invested at the risk-free rate until maturity of the options.

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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Suppose that the price of a stock today is at $25. For a strike price of K = $24 a 3-month European call option on that stock is quoted with a price of $2, and a 3-month European put option on the same stock is quoted at $1.5 Assume that the risk-free rate is 10% 3. per annum. (a) Does the put-call parity hold?
The price of a non-dividend-paying stock is $50 and the price of a 4-month European call option on the stock with a strike price of $50 is $3. The risk-free rate is 4% per annum. The price of the corresponding 4-month European put option with same strike price is $2. Establish which of the following options is true. O I. None of the above. O II. There are arbitrage opportunities because the put-call parity relation does not hold. The arbitrage opportunity is given by selling short the put option and the stock and buying the call option. The proceeds of this strategy are invested at the risk-free rate until the expiration date. O II There are no arbitrage opportunities as the put-call parity relation holds. O IV. There are arbitrage opportunities because the put-call parity relation does not hold. The arbitrage opportunity is given by selling short the call option and borrowing money from the bank at the risk-free rate to buy the stock and put option.
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.
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.
In a financial market a stock is traded with a current price of 50. Next period the price of the stock can either go up with 30 per cent or go down with 25 per cent. Risk-free debt is available with an interest rate of 8 per cent. Also traded are European options on the stock with an exercise price of 45 and a time to maturity of 1, i.e. they mature next period. Does put-call parity hold? Explain.
The price of a European call option on a non dividend paying stock with a strike price of $79 is $8. The stock price is $75, the continuously compounded risk-free rate (all maturities) is 4.50% and the time to maturity is one year. a. What is the price of a one year European put option on the stock with a strike price of $79? (Hint: Use the Put-Call Parity Formula).
The price of a one-year European call option on a non-dividend-paying stock is $6. The price of a one-year European put option on the same stock is $1. The strike price for both the call and the put is $50. The stock price today is $51 and the continuously compounded risk-free rate is 6% per annum. Use the put-call parity to suggest an arbitrage strategy to earn risk-free profits. Specifically, describe the various short and long positions you need to take in the underlying assets and show all the relevant cash flows from this strategy at both origination and expiration. Use a TABLE to show all of your work.
Assume the price of an non-dividend stock is $40, the annual volatility of the stock is 20%, and the continuous compound risk-free interest rate is 5%. What's the price of a European put option on this stock with delivery price of $40 with 1-year expiration? (The standard normal distribution table is in the attachment or you can use excel function NORMSDIST, and please keep the results with 3 decimal places.) (BS Model-Option Pricing)
The stock price 6 months from the expiration of an option is $42, the exercise price of the option is $40, the risk-free rate is 10% per annum, and the volatility is 20% per annum. a) What is the price on a European call? b) What is the price of a European put? c) Check the put-call parity is satisfied.
Consider a European call option and a European put option that have the same underlying stock, the same strike price K = 40, and the same expiration date 6 months from now. The current stock price is $45. a) Suppose the annualized risk-free rate r = 2%, what is the difference between the call premium and the put premium implied by no-arbitrage? b) Suppose the annualized risk-free borrowing rate = 4%, and the annualized risk-free lending rate = 2%. Find the maximum and minimum difference between the call premium and the put premium, i.e., C − P such that there is no arbitrage opportunities.
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.
Using put-call parity formula, derive expressions for the lower bounds for European call and put options. What is a lower bound for the price of (i) a three-month call option on a non-dividend-paying stock when the stock price is R860, the strike price is R760, and the risk-free interest rate is 10% per annum? (ii) a three-month European put option on a non-dividend-paying stock when the stock price is R500, the strike price is R610, and the discrete risk-free interest rate is 9% per annum?

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