Question

A three month American call option on MSFFT with a strike of $20/share is currently at-the –money and trading at $3.01. MSFFT has announced a dividend of $1/share to be paid four months later. Your firm intends to write a new derivative on MSFFT today: it is a three month European put with a strike of $20. As a derivatives expert you are called to price the new derivative if you know that the risk free rate is 10% per annum compounded continuously. How much should the new derivative be sold for if the market does not allow for arbitrage? Explain carefully.

Answer 1

Using put call parity
Price of European put=Price of European Call-Price of Stock+Strike Price*e^(-rate*time to expiry)+Present Value of Dividends=3.01-20+20*e^(-10%*3/12)+1*e^(-4/12)=3.23