1. Suppose a non dividend paying stock is currently priced at S = $50 and has a volatility of 60%.

(a) Risk-free three-month zero-coupon bonds with faces of $1 million are trading at $985,111.94. What is the three-month continuously compounded risk-free rate?

(b) For European call options struck at 47.09, 50, and 53.09, what do the replicating portfolios currently hold, and how much do they each cost?

(c) If the yield curve is flat, and the stock suddenly announces (unexpectedly) that it will pay a dividend of $1.01 in two months, what are the prices of the calls above (i.e., three-month European calls with the three strikes)?

(d) In each case, compare the actual loss experienced by the call owner to the call deltas. How do they compare?