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.Comment: 26 page
