a)Let Cgap(K1,K2) and Pgap(K1,K2) be the price of a gap call option and a gap put option expiring at date T written on a stock with current price S, with strike price K1 and payment trigger K2 respectively. Suppose the stock pays continuous dividend at a rate , and the continuously compounded risk-free interest rate is r. Prove the following put-call parity for gap options:

Cgap(K1,K2)Pgap(K1,K2)=S0eT K1erT.

b)Consider a 3-month European gap put option on a stock. You are given that:

1. (i) The current stock price is 75.

2. (ii) The strike price is 78.

3. (iii) The volatility of the stock is 25%.

4. (iv) The stock pays continuous dividends proportional to its price at a rate of 2%.

5. (v) The continuously compounded risk-free interest rate is 5%.

6. (vi) A 3-month European gap call option having the same strike price and payment trigger is cost 1.89.

Determine the price of the gap put option.