Weighted Monte Carlo: A New Technique for Calibrating Asset-Pricing Models

Posted: 12 Feb 2011

See all articles by Marco Avellaneda

Marco Avellaneda

New York University (NYU) - Courant Institute of Mathematical Sciences; Finance Concepts LLC

Robert Buff

affiliation not provided to SSRN

Craig A. Friedman

TIAA-CREF

Nicolas Grandechamp

affiliation not provided to SSRN

Lukasz Kruk

affiliation not provided to SSRN

Joshua Newman

affiliation not provided to SSRN

Date Written: 2001

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.

Suggested Citation

Avellaneda, Marco and Buff, Robert and Friedman, Craig A. and Grandechamp, Nicolas and Kruk, Lukasz and Newman, Joshua, Weighted Monte Carlo: A New Technique for Calibrating Asset-Pricing Models (2001). International Journal of Theoretical and Applied Finance, Vol. 4, No. 1, 2001, Available at SSRN: https://ssrn.com/abstract=1759452

Marco Avellaneda

New York University (NYU) - Courant Institute of Mathematical Sciences ( email )

251 Mercer Street
New York, NY 10012
United States
212-998-3129 (Phone)
212-995-4121 (Fax)

Finance Concepts LLC ( email )

590 Madison Avenue
21st Floor
New York, NY 10022
United States

HOME PAGE: http://www.finance-concepts.com

Robert Buff

affiliation not provided to SSRN

Craig A. Friedman (Contact Author)

TIAA-CREF ( email )

730 3rd Ave
New York, NY 10017
United States

Nicolas Grandechamp

affiliation not provided to SSRN

Lukasz Kruk

affiliation not provided to SSRN

Joshua Newman

affiliation not provided to SSRN

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