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 |
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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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