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). Assuming the strike price of a European call option on this security is $150, compute the possible payoffs of the call option given that the option expires in two periods. It may help to sketch a diagram of the possible security price movement over two periods. c). What is the expected value of the payoff of the call option?
d). What should the no-arbitrage price of the call option be?
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). Assuming the strike price of a European call option on this security is $150, compute the possible payoffs of the call option given that the option expires in two periods. It may help to sketch a diagram of the possible security price movement over two periods. c). What is the expected value of the payoff of the call option?
d). What should the no-arbitrage price of the call option be?
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). Assuming the strike price of a European call option on this security is $150, compute the possible payoffs of the call option given that the option expires in two periods. It may help to sketch a diagram of the possible security price movement over two periods. c). What is the expected value of the payoff of the call option?
d). What should the no-arbitrage price of the call option be?

Explanation / Answer

Assuming 1 period model
a
p=(e^(0*1)-1/2)/(2-1/2)=1/3
q=1-p=2/3
b
c
=(1/3*max(2*100-150,0)+2/3*max(1/2*100-150,0))=16.67
d
=(1/3*max(2*100-150,0)+2/3*max(1/2*100-150,0))*e^(-0*1)=16.67

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