文档介绍：January 15, 2001 15:19 WSPC/104-IJTAF S0219024901000882
International Journal of Theoretical and Applied Finance
Vol. 4, No. 1 (2001) 91–119
c World Scientific pany
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 Kullback–Leibler 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-
crete 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.
1. Introduction
According to basic asset-pricing theory, security prices should be equal to the ex-
pectations of their discounted cashflows under a suitable probability measure. This
“risk-neutral” measure represents the economic value of consuming one unit of ac-
count on a given future date and state of the economy. A risk-neutral probability
impl