QUESTION 5 (1+ 6 + 3 = 10 marks) Consider a stock currently priced at $100. The market expects the volatility of the stock over the next year to be 25%. The risk-free rate is 6.5% p.a. continuously compounded and a dividend of $5.50 is expected in 4 months. There are no exchange traded options available. Assume you work for a bank and have a client with a short position in 1000 units of the stock. The client wants to buy 1000 over-the-counter (OTC) calls with a strike of $105 and maturity of 12 months. Each call is on one unit of the underlying.

a) Why do you think the client wants to buy the calls? [1 mark]

b) Using an appropriate continuous time option pricing model, quantify the extra cost to the client if you give them the right to exercise the options early. [6 marks]

c) Comment on any risks associated with the clients strategy and outline any other advice on how they could manage their exposure. [3 marks]