Euler Scheme and Tempered Distributuions

Details Euler Scheme and Tempered Distributuions Euler Scheme and Tempered Distributuions

2007-07-09

arxiv.org/abs/0707.1243v1

Stochastic Processes and their Applications 116, 6 (2006) 877-904

Mathematics

Probability

26 pages

Scientific paper

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.

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