1.

a) In your own words outline the concepts underlying put-call parity.

b) Consider a 9-month European call option with a strike of $80 that is written against a non-dividend paying stock. At t=0, the call is priced at $14, and the stock is valued at $85. An otherwise equivalent put is priced at $2. Assuming a continuously compounded risk-free rate of 5% p.a., demonstrate (show) an appropriate arbitrage where the mispricing is realised immediately (i.e., at time t=0).

Now consider otherwise equivalent American calls and puts priced at $5 and $2 respectively.

c) Is an arbitrage possible? If so, show how it may be established at time t=0.

d) Now assume the stock price falls to $70 the next day and the arbitrageur is forced to close out. Show the associated cashflows.