You buy a share of stock, write a one-year call option with a strike price X = $11, and buy a one-year put option with a strike price X = $11. Your net initial cost to establish the entire portfolio is $10.50. What must be the risk-free interest rate from now until the options maturity date? The stock pays no dividends. (Do not round intermediate calculations. Enter your answer as a percentage rounded to two decimal places.) Risk-free rate

You buy a share of stock, write a one-year call option with a strike price X = $11, and buy a one-year put option with a strike price X = $11. Your net initial cost to establish the entire portfolio is $10.50. What must be the risk-free interest rate from now until the options maturity date? The stock pays no dividends. (Do not round intermediate calculations. Enter your answer as a percentage rounded to two decimal places.) Risk-free rate

EBK CONTEMPORARY FINANCIAL MANAGEMENT

14th Edition

ISBN:9781337514835

Author:MOYER

Publisher:MOYER

Chapter8: Analysis Of Risk And Return

Section: Chapter Questions

Problem 25P

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In 1973, Fischer Black and Myron Scholes developed the Black-Scholes option pricing model (OPM). (1) What assumptions underlie the OPM? (2) Write out the three equations that constitute the model. (3) According to the OPM, what is the value of a call option with the following characteristics? Stock price = 27.00 Strike price = 25.00 Time to expiration = 6 months = 0.5 years Risk-free rate = 6.0% Stock return standard deviation = 0.49
You buy a share of stock, write a 1-year call option with X = $10, and buy a 1-year put option with X = $10. Your net outlay to establish the entire portfolio is $9.50. (a) What is the payoff of your portfolio? (b) What must be the risk-free interest rate? The stock pays no dividends.
You buy a share of stock, write a one-year call option with X = $26, and buy a one-year put option with X = $26. Your net outlay to establish the entire portfolio is $24.60. What is the payoff of your portfolio? What must be the risk-free interest rate? The stock pays no dividends. (Do not round intermediate calculations. Round "risk-free rate" to 2 decimal places.)
A non – dividend – paying stock with a current price of $52, the strike price is $50, the risk free interest rate is 12% pa, the volatility is 30% pa, and the time to maturity is 3 months? a) Calculate the price of a call option on this stock b) What is the price of a put option price on this stock? c) Is the put-call parity of these options hold?
Currently you own no stock or options. Today's data for Green Corporation, where the call and put have the same exercise price and expire in one year: Strike Price Put Price Call Price Stock Price $32.50 $2.85 $1.65 $30.00 a. If you construct a protective put strategy, which securities will you buy or sell, and what is your total investment today? If the stock price is $20 on the expiration date, what will be the value of your portfolio (payoff) on that day, and your net profit? b. If you construct a covered call strategy, which securities will you buy or sell, and what is your total investment today? If the stock price is $45 on the expiration date, what will be the value of your portfolio (payoff) on that day, and your net profit?
Suppose the 1-year futures price on a stock-index portfolio is 1,914, the stock index currently is 1,900, the 1-year risk-free interest rate is 3%, and the year-end dividend that will be paid on a $1,900 investment in the market index portfolio is $40.a. By how much is the contract mispriced?b. Formulate a zero-net-investment arbitrage portfolio and show that you can lock in riskless profits equal to the futures mispricing.c. Now assume (as is true for small investors) that if you short sell the stocks in the market index, the proceeds of the short sale are kept with the broker, and you do not receive any interest income on the funds. Is there still an arbitrage opportunity (assuming that you don’t already own the shares in the index)? Explain.d. Given the short-sale rules, what is the no-arbitrage band for the stock-futures price relation-ship? That is, given a stock index of 1,900, how high and how low can the futures price be without giving rise to arbitrage opportunities?
Suppose that call options on ExxonMobil stock with time to expiration 6 months and strike price $87 are selling at an implied volatility of 27%. ExxonMobil stock price is $87 per share, and the risk-free rate is 6%. Required: If you believe the true volatility of the stock is 31%, would you want to buy or sell call options? Now you want to hedge your option position against changes in the stock price. How many shares of stock will you hold for each option contract purchased or sold?
The current price of a stock is $33, and the annual risk-free rate is 3%. A call option with a strike price of $29 and with 1 year until expiration has a current value of $7.04. What is the value of a put option written on the stock with the same exercise price and expiration date as the call option? Do not round intermediate calculations. Round your answer to the nearest cent. $
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In an efficient market, a one-year call option on stock S with K = $25 is traded at$7.06, the current stock price S0 = $28.5, the expected market return is 7.5% and the T-Bill yield is 4%. You are about to purchase a one-year put option on the same stock with K = $26, someone offered it to you at a price of $3.6. Should you buy it?
You are interested to value a put option with an exercise price of $100 and one year to expiration. The underlying stock pays no dividends, its current price is $100, and you believe it either increases to $120 or decreases to $80. The risk-free rate of interest is 10%. Calculate the put option's value using the binomial pricing model, presenting your calculations and explanations as follows: a. Draw tree-diagrams to show the possible paths of the share price and put payoffs over one year period. (Note: Show the numbers that are known and use letter(s) for what is unknown in your diagrams.) b. Compute the hedge ratio. c. Find the put option price. Explain your calculations clearly. d. Use put-call parity, find the price of a call option with the same exercise price and the same expiration date.
You are attempting to value a call option with an exercise price of $108 and one year to expiration. The underlying stock pays no dividends, its current price is $108, and you believe it has a 50% chance of increasing to $136 and a 50% chance of decreasing to $80. The risk-free rate of interest is 10%. Calculate the call option's value using the two-state stock price model. Note: Do not round intermediate calculations. Round your final answer to 2 decimal places.