c.Consider a call option with an exercise price of $105 and one year to expiration. The underlying stock pays no dividends and its current price is $100. The (risk-neutral) probabilities are a 50% chance of the stock price increasing to $130 and a 50 % chance of the stock price falling to $80. The risk free rate of interest is 4.75 % (per period). Determine the value of the option using the one- period binomial option pricing model.

c.Consider a call option with an exercise price of $105 and one year to expiration. The underlying stock pays no dividends and its current price is $100. The (risk-neutral) probabilities are a 50% chance of the stock price increasing to $130 and a 50 % chance of the stock price falling to $80. The risk free rate of interest is 4.75 % (per period). Determine the value of the option using the one- period binomial option pricing model.

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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Similar questions

A call option with an exercise price of $10 and 3 months to maturity has a price offer of $0.75. The stock price is $10.90 and the risk-free rate is 5%. Is this a boundary violation? If so, calculate the arbitrage profit available.
Using the Black-Scholes model find the premium on a call option with an exercise price of $50 on a share currently priced at $40. Assume the riskless rate of 1% per annum and the option has two years to expiration. The risk of the stock is measured by a σ value of 0.15. Decompose the premium into intrinsic value and time value? By how much is the call option priced above minimum value? Repeat the exercise for a current share price of $60.
Using the binomial call option model to find the current value of a call option with a $25 exercise price on a stock currently priced at $26. Assume the option expires at the end of two periods, the riskless interest rate is ½ percent per period. What are the hedge ratios?
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.
An option has a 40% (actuarial) chance of paying $7.03 when the underlying asset increases by 6.3% and a 60% (actuarial) chance of paying $8.67 if the underlying asset declines by 10.8%. Given that the risk-free rate is 3.6% p.a. and there are 3 months until this option is to expire, what is the risk-neutral price of this option? Answer:
Consider a put option written on an underlying security that has a current value of $100 and has a volatility of 25% (i.e. .25). The put has a strike price of $100 and expires in 1 year. The risk-free rate is 3% (.03). If the time to expiration is changed from 1 to 2 to 3 years, what happens to the value of vega (the change in the put value given a percentage point change in the volatility – say from 25% to 26%)? (Note: vega is defined in note N16 on page 8; see ). What is the comparison of the change in vega (given a change from 1 to 2 to 3 years to expiration) if the strike price is $105 (relative to if the strike is $100)?
Consider a put option on a stock that curretly sclls for £100, but may rise to £120 or fall to £80 after 1 year. The risk free rate of return is 10%, and the exercise price is £90. (a) Calculate the value of the put option using the risk-neutral valuation relationship (RNVR). Explain the reasoning behind your calculations. (b) Calculate the value of the put option by using first principles (No Arbitrage prin- ciples). Explain the reasoning behind your calculations. (c) What is the price of a call option on the same stock with the same exercise price and the same expiration date? Explain the reasoning behind your calculations.
Consider a put option whose underlying asset is a stock index with 6 months to expiration and a strike price of $1000. Suppose the risk-free interest rate for the six months is 2% and that the option’s premium is $74.20. (a) Find the future premium value in six months. (b) What is the buyer’s profit is the index spot price is $1100? (c) What is the buyer’s profit is the index spot price is $900 Only typed answer
Assume that K=61, St =65, t = 0.25 (i.e. time to expiry is 3 months), and the risk-free rate is 0.04. The current price of the put option is p = 4. If the price of the call option is 7.17, describe the arbitrage that would be possible, and calculate the profit that would result.
Assume that the value of a call option using the Black-Scholes model is $8.94. The interest rate is 8 percent, and the time to maturity is 90 days. The price of the underlying stock is $47.38, and the exercise price is $45. Calculate the price of a put using the put-call parity relationship.
You are attempting to value a put option with an exercise price of $102 and one year to expiration. The underlying stock pays no dividends, its current price is $102, and you believe it has a 50% chance of increasing to $121 and a 50% chance of decreasing to $83. The risk-free rate of interest is 10%. Calculate the value of a put option with exercise price $102.
You are attempting to value a put 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 $122 and a 50% chance of decreasing to $94. The risk-free rate of interest is 11%. Calculate the value of a put option with exercise price $108. Note: Do not round intermediate calculations. Round your answer to 2 decimal places.

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