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

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...

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Publication date:
2005-01-01
URN:
uuid:5adb9d0d-3bfa-4217-9e46-a2c77465074d
Local pid:
oai:eprints.maths.ox.ac.uk:582

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