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International Journal of Theoretical and Applied Finance Vol. 4, No. 1 (2001) 91119
 

Summary: International Journal of Theoretical and Applied Finance
Vol. 4, No. 1 (2001) 91­119
c World Scientific Publishing Company
WEIGHTED MONTE CARLO: A NEW TECHNIQUE FOR
CALIBRATING ASSET-PRICING MODELS
MARCO AVELLANEDA, ROBERT BUFF, CRAIG FRIEDMAN,
NICOLAS GRANDECHAMP, LUKASZ KRUK and JOSHUA NEWMAN
Courant Institute of Mathematical Sciences, New York University,
251 Mercer Street, New York, NY 10012, USA
Received 2 September 1999
Accepted 4 January 2000
A general approach for calibrating Monte Carlo models to the market prices of bench-
mark 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 Kullback­Leibler relative en-
tropy 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 sig-
nificant reduction of variance is demonstrated theoretically as well as numerically. Con-

  

Source: Avellaneda, Marco - Department of Mathematics, Courant Institute of Mathematical Sciences, New York University

 

Collections: Mathematics