30 Points) Assume the stock price S(t) follows a Geometric Brownian motion with a deterministic nstantaneous volatility in the risk neutral measure P and interest rate r is zero, i.e., S(t)dS(t)=(t)dW(t) (a) (15 Points) (Put Call Symmetry) Use Change of Numeraire technique to prove the following identity for the prices of European call and put options KC(S(0),K)=KP(S(0),K) where KK=S2(0) (b) (15 Points) A down-and-in call option with strike K and barrier level H is a knock-in option which has the same payoff as a European call option at expiry T if the spot price S(t) hits the barrier H at any time before or at expiry. Otherwise it pays 0 . Assume H