We know for the put-call-parity that an European call is equivalent to an Europe

Question

We know for the put-call-parity that an European call is equivalent to an European put plus

a future that have the same strike price and maturity assuming the underlying stock pays no

dividends. Write down an explicit portfolio to take advantage of the arbitrage opportunity when

ct - pt < St - K*exp(-r(T-t)). Also, what would the put-call parity be if the stock pays dividend

with Dt being the present value of all known dividends paid between now (i.e. time t) and the

expiration date. In fact, this also tells us the price of a future contract at time t that expires at

a later time T on a stock with price St that paying dividends in a continuous way with annual

rate D and the riskless annual rate is r.

Explanation / Answer

Put-call parity formula is that ;protective put (long put + long stock) must equal a long call plus a long bond. +p +S = +c +K*exp(-rT). Below are 2 sample scenarios:- p = c - S + K*exp(-rT); long put (+p) should = long call (+c) & short stock (-S) & long bond (+K is lend cash), or c = p + S - K*exp(-rT) long call (+c) should = long put (+p) & long stock (+S) & short bond (-K is borrow cash) In the example given in the question we have c - p

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