Efficient Derivative Pricing by Extended Method of Moments
72 Pages Posted: 4 Mar 2005
Date Written: January 2005
In this paper we consider an incomplete market framework and explain how to use jointly observed prices of the underlying asset and some derivatives written on this asset for an efficient pricing of other derivatives. This question involves two types of moment restrictions, which can be written either for a given value of the conditionning variable , or can be unform with respect to this conditionning variable. This distinction between local and uniform conditional moment restrictions leads to an extension of the Generalized Method of Moments, a method in which all restrictions are assumed uniform. We derive the (kernel) nonparametric efficiency bound for estimating a conditional moment of interest and prove the asymptotic efficiency of the Extended Method of Moments. The general results are applied in a stochastic volatility model to get efficient derivative asset prices.
Keywords: Generalized Method of Moments, Derivative pricing, Stochastic Volatility
JEL Classification: C13, C14, G12
Suggested Citation: Suggested Citation