Question

Consider a one-step binomial tree on stock with a current price of $100 that can go either up to $115 or down to $85 in 1 year. The stock does not pay dividend and interest rates are zero. Compute the payoff of a 1-year $100-strike European put option on the stock if the stock price ends up at the $115 node of the tree in 1 year.

Answer 1

A put option is a right to sell the underlying at an agreed price set today.

Clearly, If the stock price goes up, a stockholder can sell the stock at a higher price in the market, therefore, the holder will exercise the option only when the market price of the stock goes below the exercise price.

So, in this case, Exercise Price, E = 100 ; Stock price at year-end S = 115

So the investor won't sell the stock at 100 therefore the option lapses.

Hence, Payoff = 0