# 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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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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Step 1

We have two options here, first is doubling and second is moving down by half. We assume that the probability of moving up and moving down be 50% each, which means equal chances for both the movements. Given that the initial price of the security is 100. Now, we will calculate the price using two period binomial tree.

Step 2

In period 1, for up move (denoted as u), we will get: 100*2=200, with probability of 50%

Step 3

In period 1, for down move (denoted as d), we wil...

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