Question 1

(a) The price of a European call option on a stock with a strike price of $50 is $6. The stock price is $51, the continuously compounded risk-free rate (all maturities) is 6% and the time to maturity is one year. A dividend of $1 is expected in six months. What is the price of a one-year European put option on the stock with a strike price of $50? (2 marks)

(b) Assume six-month forward price of XYZ stock is $58. The stock pays no dividends. The six-month continuously compounded rate of interest is 4%. If the price of a put option is $3 what will be the maximum possible exercise price X that is consistent within no arbitrage context?(3 marks)

Question 2 The current price of a non-dividend-paying stock is $40. Over the next year it is expected to rise to $42 or fall to $37. An investor buys put options with a strike price of $41. Explain the number of shares necessary and the condition required to hedge the position? (4 marks)

NOTE: Please show all your workings and explain clearly your answersfor all the questions. Thank you.