Euler Scheme and Tempered Distributuions
Probability
2007-07-10 v1
Abstract
Given a smooth R^d-valued diffusion, we study how fast the Euler scheme with time step 1/n converges in law. To be precise, we look for which class of test functions f the approximate expectation E[f(X^{n,x}_1)] converges with speed 1/n to E[f(X^x_1)]. If X is uniformly elliptic, we show that this class contains all tempered distributions, and all measurable functions with exponential growth. We give applications to option pricing and hedging, proving numerical convergence rates for prices, deltas and gammas.
Cite
@article{arxiv.0707.1243,
title = {Euler Scheme and Tempered Distributuions},
author = {Julien Guyon},
journal= {arXiv preprint arXiv:0707.1243},
year = {2007}
}
Comments
26 pages