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Article Dans Une Revue Stochastic Processes and their Applications Année : 2006

Euler Scheme and Tempered Distributuions

Résumé

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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Dates et versions

hal-00160578 , version 1 (09-07-2007)

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Julien Guyon. Euler Scheme and Tempered Distributuions. Stochastic Processes and their Applications, 2006, 116 (6), pp.877-904. ⟨hal-00160578⟩
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