Assume the Black-Scholes framework. Consider a special forward start option which, 2 years from today, will give its owner a 1-year 100-strike European gap call option whose payment trigger is equal to the stock price at that time.

You are given:

(i) The gap call option is on a stock that pays dividends continuously at a rate proportional to its price. The dividend yield is 2.5%.

(ii) The current price of the stock is 100.

(iii) The stock’s volatility is 24%.

(iv) The continuously compounded risk-free interest rate is 6%.

Calculate the current price of the special forward start option.