Improving Modified Gauss-Seidel method for solving Black- Scholes PDE using Crank-Nicolson approach

Koh, Wei Sin (2008) Improving Modified Gauss-Seidel method for solving Black- Scholes PDE using Crank-Nicolson approach. Universiti Malaysia Sabah. (Unpublished)

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Abstract

In this study, Black-Scholes PDE is solved in the problem of valuation of European Put Option. The PDE is discretized by implicit and Crank-Nicolson schemes. Then, the option value is approximated by using Improving Modified Gauss-Seidel (IMGS) method and is compared with Modified Gauss-Seidel (MGS) method. The classical Gauss-Seidel (GS) method plays the role as the control method. The approximations are tested with grid sizes of 512,1024,2048,4096 and 8192. By numerical experiments, IMGS method is more superior in terms of number of iteration and computational time. The result is more accurate when IMGS is used with Crank- Nicolson approach.

Item Type: Academic Exercise
Uncontrolled Keywords: Black-Scholes PDE, implicit, Crank-Nicolson scheme, Improving Modified Gauss-Seidel, control method
Subjects: Q Science > QA Mathematics
Divisions: SCHOOL > School of Science and Technology
Depositing User: MDM SITI AZIZAH IDRIS
Date Deposited: 25 Feb 2014 06:57
Last Modified: 12 Oct 2017 04:18
URI: http://eprints.ums.edu.my/id/eprint/8351

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