Year

2014

Degree Name

Master of Science - Research

Department

School of Mathematics and Applied Statistics

Abstract

This thesis investigates the pricing of European-style options under the CGMY model, which can fit the empirically observed data in financial market better than the B-S (Black-Scholes) model. Under this model, the price of options is governed by a FPDE (fractional partial differential equation) with two spatial-fractional derivatives defined in the Weyls sense. In comparison with the derivative of integer order, the fractional-order derivative requires the function value over the entire domain rather than its value at one particular point. This has added an additional degree of diffculty when either the analytical solution or the numerical method is attempted. Albeit difficult, we have managed to derive a closed-form analytical solution for European options under the CGMY model. Based on the solution, we further discuss its asymptotic behaviors and the put-call parity under the adopted CGMY model. Finally, we propose an efficient numerical evaluation technique for the current formula so that it can be easily used in trading practice.

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