4. (a) Suppose Tom bought one share of a stock at $10, one call option with exercise price $12, and one put option with exercise price $9. Both options cost $1 and expire at time T. Draw the graph of the profit versus the stock price S(T) (10 marks] (b) Prove that for all t K-S(t), where p(t) is the put option price at time t, K is the strike price and S(t) is the stock price at time t. (10 marks] (c) Suppose at time t, the stock price is $80. A put option with exercise price $82 costs $1.5. Is there any arbitrage opportunity? Explain why. [10 marks] Solution