You own one share of a nondividend-paying stock. Because you worry that its price may drop over the next year, you decide to employ a rolling insurance strategy, which entails obtaining one 3-month European put option on the stock every three months, with the first one being bought immediately.

You are given:

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

(ii) The stock’s volatility is 30%.

(iii) The current stock price is 45.

(iv) The strike price for each option is 90% of the then-current stock price.

Your broker will sell you the four options but will charge you for their total cost now.

Under the Black-Scholes framework, how much do you now pay your broker?

(A) 1.59

(B) 2.24

(C) 2.86

(D) 3.48

(E) 3.61