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. a) Find prices of Arrow-Debreu securities. b) Calculate the price of a call option by constructing and pricing a replicating portfolio.

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. a) Find prices of Arrow-Debreu securities. b) Calculate the price of a call option by constructing and pricing a replicating portfolio.

EBK CONTEMPORARY FINANCIAL MANAGEMENT

14th Edition

ISBN:9781337514835

Author:MOYER

Publisher:MOYER

Chapter8: Analysis Of Risk And Return

Section: Chapter Questions

Problem 20P

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In a financial market a stock is traded with a current price of 50. Next period the priceof the stock can either go up with 30 per cent or go down with 25 per cent. Risk-freedebt is available with an interest rate of 8 per cent. Also traded are European optionson the stock with an exercise price of 45 and a time to maturity of 1, i.e. they maturenext period.i) Find prices of Arrow-Debreu securities.
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. 1. Find prices of Arrow-Debreu securities. 2. Calculate the price of a call option by constructing and pricing a replicating portfolio. 3. Calculate the price of a put option by RNVR. 4. Does put-call parity hold? Explain. 5. Construct one long strap and one long straddle using any options from previous part. Sketch the profit and loss graph for each of your portfolios separately and explain the similarity and difference between two positions.
In a financial market a stock is traded with a current price of 50. Next period the priceof the stock can either go up with 30 per cent or go down with 25 per cent. Risk-freedebt is available with an interest rate of 8 per cent. Also traded are European optionson the stock with an exercise price of 45 and a time to maturity of 1, i.e. they maturenext period.i) Find prices of Arrow-Debreu securities.ii) Calculate the price of a call option by constructing and pricing areplicating portfolio.
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. Calculate the price of a put option by RNVR.
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. Calculate the price of a call option by constructing and pricing a replicating portfolio.
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.
ANSWER C AND D PLEASE ONLY In a financial market a stock is traded with a current price of 50. Next period the priceof the stock can either go up with 30 per cent or go down with 25 per cent. Risk-freedebt is available with an interest rate of 8 per cent. Also traded are European optionson the stock with an exercise price of 45 and a time to maturity of 1, i.e. they maturenext period.a) Find prices of Arrow-Debreu securities.b) Calculate the price of a call option by constructing and pricing areplicating portfolio. c) Calculate the price of a put option by RNVR.d) Does put-call parity hold? Explain.
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 this problem, we derive the put-call parity relationship for European options on stocks that pay dividends before option expiration. For simplicity, assume that the stock makes one dividend payment of $D per share at the expiration date of the option.a. What is the value of a stock-plus-put position on the expiration date of the option?b. Now consider a portfolio comprising a call option and a zero-coupon bond with the same maturity date as the option and with face value (X + D). What is the value of this portfolio on the option expiration date? You should find that its value equals that of the stock-plus-put portfolio regardless of the stock price.c. What is the cost of establishing the two portfolios in parts (a) and (b)? Equate the costs of these portfolios, and you will derive the put-call parity relationship.
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 an european call option on a stock that is not paying dividends with the following characteristics. (i) The stock price at t = 0 is S = $30. (ii) The stricke price is $31. (iii) The volatility of the stock is 20%. (iv) The free risk interest rate is 7%. Construct a 2 period recombining Binomial tree diagram and specty tne varue or the can optron at eacn node of the tree diagram.
Consider a European call on Procter and Gamble stock (PG) that expires in one period. The current stock price is $120, the strike price is $130, and the risk-free rate is 5%. Assume that PG stock will either go up to $150 (probability = .4), or go down to $90 (probability = .6). Construct a replicating portfolio based on shares of PG stock and a position in a risk-free asset, and compute the price of the call option.