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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 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


Solution Summary

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.