Suppose that, in each period, the cost of a security either goes up by a factor

Question

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. a). Compute the risk neutral probabilities p (price moves up) and q = 1 p (price moves down) for this model. b). Sketch a diagram of this two period stock price model. 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. d). What is the expected value of the payoff of the call option? e). What should the no-arbitrage price of the call option be?

Explanation / Answer

for neutral probability

100*2*p+50*(1-p)=100

as in one case it gets doubled and other case it is halved

p=1/3 q=1-p=2/3

*possible pay off is either 100 or -50

*expected payoff is 180*p+45*(1-p)

as in one case it gets doubled and other case it is halved

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