A)Three put options on a stock have the same expiration date and strike prices of 55, 60 and 65. The market prices are 3, 5 and 8 respectively. Explain how a butterfly spread can be created. Construct a table showing the profit from the strategy. Demonstrate for what range of stock prices the butterfly spread would lead to a loss.

B) A stock price is currently $40. Over each of the next two three-month periods, it is expected to go up by 10% or down 10%. The risk-free interest rate is 12% per annum with continuous compounding. Calculate the value of a six-month European put option with a strike price of $42 using a binomial tree

C) A European put option has an exercise price of 100. It has one year to expiration. The underlying stock does not pay any dividends and has a current price of 90. This price has a 50% chance of increasing to 110 and a 50% chance of decreasing to 70. The risk free rate of interest is 1% p.a. Calculate the price of the put option using the two state stock price model applying the replicating portfolio method.

D) A four-month European call option on a stock that does not pay dividends is currently selling for 5. The stock price is 64 and the strike price is 60. The risk-free rate of interest is 12% p.a. for all maturities. What opportunities, if any, are there for an arbitrageur? Demonstrate. Assume continuous compounding throughout.

E)Show what happens to the price of a put option in the Black-Scholes model when N(-d1) and N(-d2) tend to 1. How is this different from when N(-d1) and N(-d2) tend to 0?. What is the interpretation therefore of N(-d1) and N(-d2)?