1. Prove the put-call parity: C(T, K) P(T, K) = St Bt(T)K, where St is the...

 

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1. Prove the put-call parity: C(T, K) P(T, K) = St Bt(T)K, where St is the price of a stock at time t, C(T,K) and P(T, K) are the prices of European call and put options on the stock at time t with strike K and maturity T, and B(T) = er(T-t) is the price of a zero-coupon bond at time t with face value $1 and maturity T. The annual interest rate r is constant. 1. Prove the put-call parity: C(T, K) P(T, K) = St Bt(T)K, where St is the price of a stock at time t, C(T,K) and P(T, K) are the prices of European call and put options on the stock at time t with strike K and maturity T, and B(T) = er(T-t) is the price of a zero-coupon bond at time t with face value $1 and maturity T. The annual interest rate r is constant.