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Mathematical Theory And Numerical Methods

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AMA 3021: Computational Finance
Business Project 2 Black-Scholes Solution by Finite Differences

Fynn McKay
(40099355)

Submission : 18th Dec 2015

School of Mathematics and Physics

Contents Executive Summary 3 Introduction 4 Question . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Background Information . . . . . . . . . . . . . . . . . 4 Overview of Solution . . . . . . . . . . . . . Applications . . . . . . . . . . . . . . . . . . Mathematical Theory and Numerical Methods Black-Scholes Model MENTION BOUNDARY FROM OX Method of Finite Differencing Numerical Accuracy Algorithm and Implementation Results and Discussion Tabulated Figures (Look at booklet, BIG) Discussion of Error Drawbacks of B-S Comparison to Published Results Conclusion Main Findings Further Considerations References

2. Introduction
2.1. Question
Write a program (in MATLAB or C/C++) to calculate the put option price p given data for the strike price X, risk-free interest rate r, volatility σ and time to expiry T.
Do this by writing the Black-Scholes Equation as a finite-difference equation and then integrating backwards in time from the expiry date to find the put price, given the current spot price.
Use the following IBM put option figures to do so;
Current IBM spot price (As of November 28th 2015): S0=£138.50
Risk-free interest rate: r=1.0% per Annum
Put option expiry:

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