The spot price of a non-dividend paying stock is recorded as t70 at the close of the day. You estimate that this price is equally likely to go up or down by 30% over the next nine months and observe that the continuously compounded annual risk-free rate is 20% per year across all maturities. Use a single-step binomial tree together with the mimicking portfolio approach to compute the theoretical price of a European call option written on this stock with a strike price of t55 and exactly nine months until expiration.

The spot price of a non-dividend paying stock is recorded as t70 at the close of the day. You estimate that this price is equally likely to go up or down by 30% over the next nine months and observe that the continuously compounded annual risk-free rate is 20% per year across all maturities. Use a single-step binomial tree together with the mimicking portfolio approach to compute the theoretical price of a European call option written on this stock with a strike price of t55 and exactly nine months until expiration.

International Financial Management

14th Edition

ISBN:9780357130698

Author:Madura

Publisher:Madura

Chapter11: Managing Transaction Exposure

Section: Chapter Questions

Problem 35QA

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User A European call option with a strike price of 105 will expire in two years. The current stock price is $ 100. The value of u = 1.3 and the value of d = 0.8. The annual interest rate (based on continuous compounding)is 10%. Using a three-period binomial model （a）Determine the risk-neutral probability values at each end node (Hint: draw a tree) Please draw a binomial tree！！！ Can you give me the steps （b）Find the expected value of the call in two years. （c）Find the current price of the call option.
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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.
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