Question

A stock S has value S = 2 today and in one year the value either doubles or halves. Assuming interest rates are zero:

(a) Show how to replicate a call option with strike at 2.5 using the stock and the riskless asset and calculate the price of the option today

(b) Similarly replicate the put option struck at 2.5 and calculate its value today.

Answer 1

a) call option is the right to buy a stock at a predetermined price at a predetermined date which can or cannot be exercised based on the market price of the stock in case this option is not exercised the buyer looses out on the premium. The stock price here will either be 4 or 1 in one year so if it is 4 the buyer should exercise the option at a strike price of 2.5 and sell the stock at 4 in the market to make a profit of 1.5.

B) put option is the right to sell a stock at a predetermined price at a predertermined date which can or cannot be exercised based on the market price of the stock in case this option is not exercised the buyer of the option will loose out on the premium. The stock price will either be 4 or 1 in a year so the buyer should exercise the put option if the price goes to 1 so that he can make a profit of 1.5 by selling the stock at the strike price of 2.5 and if required can buy it back at 1 from the market.