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 expiration date T, and dividends are paid.
a) Assume a no-arbitrage market without transaction costs. Show the put call parity
S + VP - VC = Ke-r(T-t)
for all t, where K is the strike price 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
Put-call parity is investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.