1. Consider a European derivative security with the following payo structure V = V (S) as a function of the underlying asset S:

V (S) =:

0, S<60

S-60, 60<=S<=70

10, 70<=S<=90

S-80, S>90

The option expires one year from today. The price of a zero coupon bond maturing one year from today is $0.99. Currently the stock price is $89 per share.

(a) Draw the payoff diagram, that is, plot V as a function of S.

(b) Suppose you are able to write (sell) this option at time 0 for $90. Create an arbitrage portfolio.

(c) Suppose you are able to buy this option at time 0 for $9. Create an arbitrage portfolio.

(d) Show how to replicate this option by a portfolio containing only stock, bonds and call options.

Please advise how should we solve this problem. Thanks!