Assume the Black-Scholes framework. Consider a special forward start option which, 1 year from today, will give its owner a 1-year European put option with a strike price equal to the one-year stock price, provided that the one-year stock price is higher than the current stock price; otherwise, the owner will receive nothing.

You are given:

(i) The European put option is on a stock that pays dividends continuously at a rate proportional to its price. The dividend yield is 2%.

(ii) The current stock price is 100.

(iii) The stock’s volatility is 30%.

(iv) The continuously compounded risk-free interest rate is 8%.

For this special forward start option, calculate:

(a) Its current price 

(b) Its current delta