In a simple one period market model consisting of a risky as

In a simple one period market model consisting of a risky asset and a risk-free asset, suppose the risky asset price satisfies S(0) = 100 and S(1) ={150. with probability 0.8. 50. with probability 0.2., Also, suppose that the risk-free asset price follows A(0) = A(1) = 100. Consider a put option with the strike price K = 100 and the maturity time T = 1. Find the initial price P(0) of this put option under the No Arbitrage assumption.

Solution

Initial price is calculated below-

Stock after one year = $150*0.8 + $50*0.2

                              = $130

Hence, the initial price = $100-$130 = -$30