## Team : mathfi

## Section: New Results

## Monte Carlo methods and stochastic algorithms

### Variance reduction methods in Monte Carlo simulations

**Participants:**B. Arouna, B. Lapeyre, N. Moreni.

Under the supervision of Bernard Lapeyre, B. Arouna has defended his PHD thesis in which he shown that stochastics algorithms can be efficiently used in order to decrease variance. He provides tractable methods of variance reduction in Monte Carlo estimation of expectations (integrals) and proves associated theoretical results. His work has been published in [13] and [14].

Nicola Moreni is studying variance reduction techniques for option pricing based on Monte Carlo simulation. In particular, in a joint project with the University of Pavia (Italy), he applies path integral techniques to the pricing of path-dependent European options. He has also deals with a variance reduction technique for the Longstaff-Schwartz algorithm for American option pricing. This technique is based on extension of the work of B. Arouna to the case of American options.

### Monte Carlo methods for American options in high dimension.

**Participants:**L. Caramellino (University of Rome II), A. Zanette.

We have done numerical comparaison between some recent Monte Carlo algorithms for pricing and hedging American options in high dimension, in particular between the quantization method of Barraquand-Martineau and an algorithm based on Malliavin calculus [30].