Question 2 (15 marks) a) Suppose a non-dividend paying stock price is $45 and a call option on this stock with a strike price of $40 expiring in 6 months is available. The risk free rate is 3% with continuous compounding and stock return volatility is 40% p.a. Calculate the call price using the Black-Scholes formula. (10 marks) [Enter your answer here] b) What is the corresponding European put price with the same strike and maturity if put-call parity holds in section (a)? (3 marks) [Enter your answer here] c) A one-month call option with a strike of $41 costs $1.5. A put option with strike of $41 costs $3.5. Both are European options with the same maturity. Explain how you can use these options to gain if you are betting purely on volatility only? What are the ranges of St that can make a profit? (4 marks) [Enter your answer here] d) By shorting corn futures contracts, can the corn farmers hedge against the risk of adverse weather yielding a lower corn output? Explain. (3 marks) [Enter your answer here] Question 2 (15 marks) a) Suppose a non-dividend paying stock price is $45 and a call option on this stock with a strike price of $40 expiring in 6 months is available. The risk free rate is 3% with continuous compounding and stock return volatility is 40% p.a. Calculate the call price using the Black-Scholes formula. (10 marks) [Enter your answer here] b) What is the corresponding European put price with the same strike and maturity if put-call parity holds in section (a)? (3 marks) [Enter your answer here] c) A one-month call option with a strike of $41 costs $1.5. A put option with strike of $41 costs $3.5. Both are European options with the same maturity. Explain how you can use these options to gain if you are betting purely on volatility only? What are the ranges of St that can make a profit? (4 marks) [Enter your answer here] d) By shorting corn futures contracts, can the corn farmers hedge against the risk of adverse weather yielding a lower corn output? Explain. (3 marks) [Enter your answer here]