The Mathematical Institute, University of Oxford, Eprints Archive

Measure order of convergence without an exact solution, Euler vs Milstein scheme

Schmitz Abe, Klaus and Shaw, William T. (2005) Measure order of convergence without an exact solution, Euler vs Milstein scheme. International Journal of Pure and Applied Mathematics, 24 (3). pp. 365-381.

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Abstract

The purpose of this paper is to measure the strong and weak order of convergence of both the Euler and Milstein schemes using a stochastic volatility model and an N−dimensional Exponential Brownian Motion Process (EBM). An exact solution is normally required to calculate the order of convergence, however there are none available for this volatility process. We propose a method to solve this problem. We also show numerically that when we apply the Milstein scheme to an N−dimensional stochastic process, there is a need to take into account the correlation between the systems.

Item Type:Article
Subjects:D - G > Game theory, mathematical finance, economics, social and behavioral sciences
Research Groups:Mathematical and Computational Finance Group
ID Code:582
Deposited By:Eprints Administrator
Deposited On:27 Mar 2007
Last Modified:20 Jul 2009 14:22

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