WEIGHTED MONTE CARLO: A NEW TECHNIQUE FOR CALIBRATING ASSET-PRICING MODELS

Marco Avellaneda, Robert Buff, Craig Friedman, Nicolas Grandechamp, Lukasz Kruk and Joshua Newman
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Marco Avellaneda: Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA
Robert Buff: Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA
Craig Friedman: Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA
Nicolas Grandechamp: Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA
Lukasz Kruk: Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA
Joshua Newman: Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA

International Journal of Theoretical and Applied Finance (IJTAF), 2001, vol. 04, issue 01, 91-119

Abstract: 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 price-misspecifications and finite-sample effects in the simulation by assigning "probability weights" to the simulated paths. The choice of weights is done by minimizing the Kullback–Leibler relative entropy distance 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. A significant reduction of variance is demonstrated theoretically as well as numerically. Concrete applications to the calibration of stochastic volatility models and term-structure models with up to 40 benchmark instruments are presented. The construction of implied volatility surfaces and forward-rate curves and the pricing and hedging of exotic options are investigated through several examples.

Date: 2001
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DOI: 10.1142/S0219024901000882

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