3. (a) Within the Binomial Tree model, describe the dynamic of the spot price and explain the risk-neutral valuation approach to valuing a European option using a one-step binomial tree. [4] (b) Explain carefully the difference between selling a call option and buying a put option. Write down the two payoffs and draw their graphs. 3 (c) A stock price is currently 37 E. Over each of the next two three-month periods it is expected to go up by 12% or down by 8%. The risk free interest rate is 4% per annum with continuous compounding. (i) What is the value of a six-month European put option on the underlying stock with a strike price of 41 E? [5] (ii) What is the value of a six-month American put option on the underlying stock with the same strike price? 5 (iii) Explain briefly what the delta of a stock option is. (iv) Calculate the delta over each step for part 3(c)i. [3] (v) Compute the price of a European call with the same underlying, strike price and maturity of the put in 3(c)i using the put-call parity