Financial Engineering – IC302
Autumn Term 2020/1
Monte Carlo Method Self-Study Exercise
This is a self-study exercise to accompany lecture 8. You are not required to complete the exercise, and there will be no seminar session dedicated to it. You may find, however that completing the exercise improves your understanding of how the Monte Carlo method is used to value derivatives. You may also find that the exercise is quite fun!
The exercise is based on the Excel workbook IC302-Monte Carlo Simulation-Que. The workbook explains how to construct a simple Monte Carlo simulation to estimate the price of a European call option. It also contains a full implementation of Monte Carlo valuation of a the option in VBA and a function to calculate the Black-Scholes-Merton value of the option. You are free to experiment with the workbook in any way you like, but I have suggested below some activities you might attempt and questions you might try to answer.
1. Use the workbook to calculate the value of a one-year European call option for the parameter values already entered in the workbook by following the instructions in the box at the top of the worksheet.
2. Use the estimated price and standard error from this simulation to calculate a 95% confidence interval for the option price.
3. Does the Black-Scholes-Merton price for this option fall within the 95% confidence interval? (You can calculate the Black-Scholes-Merton price using the function in the box on the lower right-hand side of the worksheet.)
4. Why is the Monte Carlo estimate of the price not the same as the Black-Scholes- Merton price? What could you do to increase the accuracy of the Monte Carlo estimate?
5. The other box on the right-hand side of the worksheet is linked to a full VBA implementation of the Monte Carlo valuation of the European call. In this implementation, you can vary the number of trials in the simulation. Approximately how many trials are needed to reproduce the Black-Scholes-Merton price, to the nearest cent or penny?