Hi, Just wondering is it acceptable to solve this question looking it from a point of view of making a profit at t=0 and then checking at the expiry date of the options if the replicating porfolio always produces the same payoff as the option? For example, as per the question we notice a arbitrage profit may exist as the put is price at 25p. So we 'buy cheap, sell expensive' and using put-call parity relationship, we sell the call and therefore we need to replicate the call using ct=pt+St-Ke^-rT. This porfolio costs or is valued at 25+123-120e^-0.06*0.25 = 29.78. So profit at t=0 =30-29.79=.2134 (sold call for 30, setup porfolio for 29.78) At time=3/12 if ST>120 ct = ST-120 porfolio = 0+ST-120*e^-0.06*0.25*e^0.06*0.25=ST-120. I assume the dividends receieved continously are reinvested in the share continously so share grows from 123 to ST. At time=3/12 if ST<120 ct=0 porfolio = 120-ST+ST-120*e^-0.06*0.25*e^0.06*0.25=0 So regardless outcome we replicate the call option and we make profits of 0.214 at t=0. Thanks, Darragh
Hi Darragh Yes, your proof also demonstrates that there is a possibility of arbitrage here. My preference would still be for the proof in the notes though as arbitrage is defined in terms of a zero initial cost portfolio. Best wishes Mark
Hi, Thanks Mark for your help, noted on your comment regarding the definition of arbitrage. Cheers, Darragh
