# 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: