Please, can you answer the questions below ? Thank you! Urgent! Exam is tomorrow

An investor buys a European put on a share for 3. The stock price is 42 and the strike price is 40. Under what circumstances does the investor make a prot if she exercises the option (ignoring the time value of money)? Draw a diagram showing the variation of the investor's prot with stock price at the maturity of the option. (5 marks) An investor sells a European call on a share for 4. The stock price is 47 and the strike price is 50. Under what circumstances does the investor make a profit if she exercises the option (ignoring the time value of money)? Draw a diagram showing the variation of the investor's profit with stock price at the maturity of the option. (5 marks) A trader buys a call option with a strike price of 45 and a put option with a strike price of 40. Both options have the same maturity. The call option costs 3 and the put option costs 4. Plot the payoff of the combination at expiration, and discuss the motivation for building the combination. (12 marks) Lancaster Motor plc (LM) shares are currently worth 20 per share. In one year, the stock price is expected to either increase by 40% or decrease by 25%. A European call option on the stock has a strike price of 23 and expires in one year. The risk-free rate is 4% per year. Use the single period binomial option pricing model to calculate the arbitrage-free price of the call option today. (6 marks) Suppose that the European call option on the same stock with the same maturity and exercise price is trading at 3 in the market, as opposed to your calculation in part (i). Are there any arbitrage opportunities? If yes, demonstrate how one can profit from this possibility. {6 marks)