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2. This question is about American Option pricing. (a) In Excel, write a VBA function called AmericanOption that values an American option using a binomial tree. The function inputs must include the option strike K, spot price of the stock S, risk-free rate r, the stock price drift μ, volatility o and years to expiry T. The other input must be the number of time steps N per year. You should also include two extra inputs. The first is called "OptionType" and can be "C" or "P" for call or put. The other input is "ExerciseType". This can be "E" or "A" for European or American. You should use these inputs in your valuation code. (b) Show that when S = 100, K = 100, r = 0.01, q = 0.06, o = 0.12 and T = 1.0 you recover the same American call option results as those in the course slides where we used N = 4. You must provide a clear and easy-to-understand listing of your code in the answer. (c) For a European call option with S= 100, K = 100, r = 0.01, q = 0.06, 0 = 0.12 and T = 1.0 show that as N increases from N = 10 to N = 120 in steps of 10 the error (tree price V(N) minus Black-Scholes price) converges towards zero. Provide a table of values and a plot of the error versus N. (d) Using the tree, calculate the delta, gamma and theta of the option. Explain how you do this. Calculate the delta, gamma and theta of the European call option and compare them to the American option values. (e) Now consider an American call option with the same characteristics but set the dividend yield q = 0. Set N = 100 and calculate the value of the option for S 80, 90, 100, 110, 120 and calculate the price difference to the value the Eu- ropean call option with the same features. Show this in a table. What does the results tell you ?