1. Suppose that, in each period, the cost of a security either goes up by a factor of u = 2 or down by a factor d = 1/2. Assume the initial price of the security is $100 and that the interest rate r is 0. c) Assuming the strike price of a European call option on this security is $90, compute the possible payoffs of the call option given that the option expires in two periods.

1. Suppose that, in each period, the cost of a security either goes up by a factor of u = 2 or down by a factor d = 1/2. Assume the initial price of the security is $100 and that the interest rate r is 0. c) Assuming the strike price of a European call option on this security is $90, compute the possible payoffs of the call option given that the option expires in two periods.

International Financial Management

14th Edition

ISBN:9780357130698

Author:Madura

Publisher:Madura

Chapter5: Currency Derivatives

Section: Chapter Questions

Problem 6BIC

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Suppose that, in each period, the cost of a security either goes up by a factor of 2 or goes down by a factor of 1/2 (i.e. u=2, d=1/2). If the initial price of the security is 100, determine the no-arbitrage cost of a call option to purchase the security at the end of two periods for a price of 150.
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I asked this question yesterday: Suppose that, in each period, the cost of a security either goes up by a factor of 2 or goes down by a factor of 1/2 (i.e. u=2, d=1/2). If the initial price of the security is 100, determine the no-arbitrage cost of a call option to purchase the security at the end of two periods for a price of 150. In the answer I got today the first step said: "We assume that the probability of moving up and moving down be 50% each, which means equal chances for both the movements. " I had learned that the risk neutral probability for the stock price to go up is: p=(1+r-d)/(u-d). In this particular problem, we'd have p=(1+0-.5)/(2-.5)=1/3. And so the probability going down would be 1-p or 2/3. Thus, my question is why weren't these probabilities used in the solution previously sent? And if they should be, what would be the new solution to the problem? Thank you for your help. I'm new to learning all of this and some of it is hard for me to understand.
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