Don't copy the other answer...

1. Prove the Black-Scholes pricing formula for puts. That is, in the Black- Scholes market, consider X = max{E - S(T),0}, the European put option with strike price E. Prove that its time t fair price is II(t) = F(t, Si(t)), where F(t, x) = Ee-"TN(-d2(t, x)) - XN(-di(t, x)), with a di(t, x) = log(8) + (r + 2)T ON log() + (1 - ) d2(t, x) = of = di(t, x) OVT. Hint. To prove this statement, you need to properly modify the proof of the Black-Scholes pricing formula for calls. [40 Marks)