Economical Numerical Methods for Solving Two-Dimensional Equations of the Black-Scholes Type

Student: Zimin Stepan

Educational Programme: Applied Mathematics and Information Science (Bachelor)

Final Grade: 10

Year of Graduation: 2016

The goal of this paper is to develop a method for pricing options on several assets under the Black–Scholes model. For this purpose we exploit an economical numerical algorithm for multidimensional parabolic partial differential equations with mixed derivatives, namely a three-level alternating direction implicit (ADI) scheme. We implement the proposed method in the case of two underlying assets (dimensions) in Matlab. We exploit the non-uniform meshes in space and time and increase efficiency of the algorithm. We also develop an efficient implementation of Monte Carlo simulation technique. A number of pricing problems including exotic ones is analyzed numerically by means of this method.

Full text (added May 26, 2016)

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