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

Marco Avellaneda, Robert Buff, Craig Friedman, Nicolas Grandchamp, Lukasz Kruk and Joshua Newman
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Marco Avellaneda: New York University, Courant Institute of Mathematical Sciences
Robert Buff: New York University, Courant Institute of Mathematical Sciences
Craig Friedman: New York University, Courant Institute of Mathematical Sciences
Nicolas Grandchamp: New York University, Courant Institute of Mathematical Sciences
Lukasz Kruk: New York University, Courant Institute of Mathematical Sciences
Joshua Newman: New York University, Courant Institute of Mathematical Sciences

A chapter in Applied and Industrial Mathematics, Venice—2, 1998, 2000, pp 1-31 from Springer

Abstract: 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 for 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 forty 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.

Keywords: Option Price; Relative Entropy; Implied Volatility; Stochastic Volatility Model; Spot Price (search for similar items in EconPapers)
Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-011-4193-2_1

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DOI: 10.1007/978-94-011-4193-2_1

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