Question

Consider a one-step binomial tree on stock with a current price of $100 that can go either up to $120 or down to $80 in 1 year. the stock does not pay dividend and interest rates are zero. we want to price the 1-year $90-strike european put option on this tree.

(i) what's the put option payoff 1 year later if the stock price ends up at $120?

Answer 1

If the stock price ends up at $120 after one year, the European put option with a strike price of $90 would be out-of-the-money, resulting in a payoff of $0.

Step-by-step explanation:

The student is asking about the pricing of a European put option using a one-step binomial tree model. In the scenario provided, the stock price can either increase to $120 or decrease to $80 in one year, and the put option has a strike price of $90. To calculate the put option payoff one year later, if the stock price ends up at $120, we consider the option would end up out-of-the-money, since the stock price is higher than the strike price, meaning the holder would choose not to exercise the option. Hence, the put option payoff in this case is $0.

The payoff of the European put option can be calculated based on the stock price at the end of the year. If the stock price ends up at $120, which is above the strike price of $90, then the put option will have a payoff of $0, as the buyer will not exercise the option since it is not profitable to sell the stock at a lower price than the market value.