Assume a stock pays no dividends and is presently selling for $80. The continuously compounded return on the stock ln(S_t/So), is distributed , with m = 25% per annum and s² = 16% per annum. The risk free rate is 14% per annum.

1. Use the Black Scholes model to value a call option on the stock with an exercise price of $75 and a maturity date 3 months hence.

S = $80, E = $75, T =1/4 yr, s² = .16

2. If you wished to replicate the payoff from the call by continually adjusting a position in the stock and a position in bonds, what position should you take today?
3. If the stock were to decrease in value overnight by $1.00, by how much would the call change in value?