Consider an option on a non-dividend-paying stock when the stock price is $28, the exercise price is $29, the risk-free interest rate is 5% per annum, the volatility is 25% per annum, and the time to maturity is four months. Using the Black-Scholes-Merton approach, What is the price of the option if it is a European call? What is the price of the option if it is an American call? What is the price of the option if it is a European put? Show that put–call parity holds.

Consider an option on a non-dividend-paying stock when the stock price is $28, the exercise price is $29, the risk-free interest rate is 5% per annum, the volatility is 25% per annum, and the time to maturity is four months. Using the Black-Scholes-Merton approach, What is the price of the option if it is a European call? What is the price of the option if it is an American call? What is the price of the option if it is a European put? Show that put–call parity holds.

Intermediate Financial Management (MindTap Course List)

13th Edition

ISBN:9781337395083

Author:Eugene F. Brigham, Phillip R. Daves

Publisher:Eugene F. Brigham, Phillip R. Daves

Chapter5: Financial Options

Section: Chapter Questions

Problem 5MC: In 1973, Fischer Black and Myron Scholes developed the Black-Scholes option pricing model...

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Consider a European call on Amazon Stock (AMZN) that expires in one period. The current stock price is $100, the strike price is $120, and the risk-free rate is 5%. Assume AMZN stock will either go up to $140 or down to $80. Construct a replicating portfolio using shares of AMZN stock and a position in a risk-free asset ... what is the value of the call option? Call Option Price = $4.84 Call Option Price = $2.95 Call Option Price = $7.93 Call Option Price = $12.04
Consider a European call on Amazon Stock (AMZN) that expires in one period. The current stock price is $100, the strike price is $120, and the risk-free rate is 5%. Assume AMZN stock will either go up to $140 or down to $80. Construct a replicating portfolio using shares of AMZN stock and a position in a risk-free asset … what is the value of the call option?
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We are looking at a European put option and a European call option written on the same underlying asset, same exercise price and same time to expiration. There is no dividend paid prior to expiration. The current stock price is $130 and the exercise price is $125. Suppose you have figured out the delta of the put option is -0.4451, what is the delta of the call option? 0.4451 0.5549 -0.5549 -0.4451
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1. Consider a family of European call options on a non - dividend - paying stock, with maturity T, each option being identical except for its strike price. The current value of the call with strike price K is denoted by C(K) . There is a risk - free asset with interest rate r >= 0 (b) If you observe that the prices of the two options C( K 1) and C( K 2) satisfy K2 K 1<C(K1)-C(K2), construct a zero - cost strategy that corresponds to an arbitrage opportunity, and explain why this strategy leads to arbitrage.
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