A. A non-dividend paying stock is trading at a price of 143.56 today. There is a call option on this stock with strike price 143 and expiration date 157 days away (assume 365 days in a year). Interest is continuous compounding at r = 2.55%. Assuming that the volatility of the stock is 35%, answer the following questions:

1. Use the Black-Scholes-Merton model to find the price of this option. (5 marks)

2. Use the put-call parity to obtain an approximate value for the price of a put option on this stock with the same strike price and maturity as the call option described above. (5 marks)

3. A bank has bought 10,000 call options with the above characteristics. What strategy should the bank take to delta-hedge this portfolio using the underlying stock? Explain what we understand by the delta of an option. (5 marks)

4. If the bank sets up this delta neutral position strategy, explain what trade is necessary to maintain delta neutrality if the price of the stock jumps to 154.71 in the first hour of trading. (5 marks)

5. Explain the main assumptions of the Black-Scholes-Merton model commenting on their plausibility. (5 marks)