Put-Call Parity Consider a portfolio consisting of three positions related to the same asset, namely, one share (price S), one European put (value VP), plus a short position of one European call (value VC). Put and call have the same expiration date T, and no dividends are paid.

a) Assume a no-arbitrage market without transaction costs. Show S + VP − VC = Ke−r(T −t)

for all t, where K is the strike and r the risk-free interest rate.

b) Use the put-call parity to show VC(S,t) ≥ S − Ke−r(T −t)

VP(S,t) ≥ Ke−r(T −t) − S .