Marco Avellaneda, Robert Buff, Craig Friedman, Nicolas Grandchamp, Lukasz Kruk and Joshua Newman

A general approach for calibrating Monte Carlo models to the market prices of benchmark securities is presented. Starting from a given model for market dynamics (price diffusion, rate diffusion, etc.), the algorithm corrects for price misspecifications and finite-sample effects in the simulation by assigning ``probability weights'' to the simulated paths. The choice of the weights is done by minimizing the Kullback-Leibler relative entropy of the posterior measure to the empirical measure. The resulting ensemble prices the given set of benchmark instruments exactly or in the sense of least-squares. We discuss pricing and hedging in the context of these weighted Monte Carlo models. Significant reduction of variance due to the model calibration is demonstrated theoretically as well as numerically. Concrete applications to the calibration of stochastic volatility models and term-structure models with up to forty benchmark instruments are presented. Implied volatilities, forward-rate curves and exotic option pricing are investigated with several examples.