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?

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.

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