Recall the multi-period binomial option pricing framework where at each time step the underlying stock price process moves either up or down by a constant proportion. Consider the following statement: "By dividing the time to maturity T into n time-steps At = Tin, and repeating the binomial stock price increment, a binomial tree is produced with a stock price and an option payoff at each of the n + 1 terminal nodes. It can be shown that for the binomial value of an option converges to the Black- Scholes value. However, the binomial option value is highly non-linear in n. The conver- gence pattern depends greatly on the ratio K/So, and for the choice of dze it is highly irregular when K * S. This makes it difficult to fix a suitable n. A better choice is dar V Now the convergence pattern is gradual for all K/S,." Illustrate the above statement by constructing an appropriate example with a European call option and implementing it in an MS Excel spreadsheet. a) Describe the example you have constructed in details and specify all the values of the parameters you use. Motivate your choice. (5 marks) b) Explain how you have implemented your illustrative example from a) in MS Excel. Plot (some of your results appropriately and write a short report (max two pages) explaining why you think they illustrate the statement (16 marks) c) Briefly discuss what you learned in completing the task, what difficulties/problems/is- sues you encountered and how you resolved them. Would you do anything differently if you were starting again? (3 marks) Recall the multi-period binomial option pricing framework where at each time step the underlying stock price process moves either up or down by a constant proportion. Consider the following statement: "By dividing the time to maturity T into n time-steps At = Tin, and repeating the binomial stock price increment, a binomial tree is produced with a stock price and an option payoff at each of the n + 1 terminal nodes. It can be shown that for the binomial value of an option converges to the Black- Scholes value. However, the binomial option value is highly non-linear in n. The conver- gence pattern depends greatly on the ratio K/So, and for the choice of dze it is highly irregular when K * S. This makes it difficult to fix a suitable n. A better choice is dar V Now the convergence pattern is gradual for all K/S,." Illustrate the above statement by constructing an appropriate example with a European call option and implementing it in an MS Excel spreadsheet. a) Describe the example you have constructed in details and specify all the values of the parameters you use. Motivate your choice. (5 marks) b) Explain how you have implemented your illustrative example from a) in MS Excel. Plot (some of your results appropriately and write a short report (max two pages) explaining why you think they illustrate the statement (16 marks) c) Briefly discuss what you learned in completing the task, what difficulties/problems/is- sues you encountered and how you resolved them. Would you do anything differently if you were starting again
