Model reduction methods in option pricing

Abstract

In this work we introduce the Proper Orthogonal Decomposition (POD)approach to the valuation of contingent claims for one?dimensional price models.First, we present the POD in the context of an abstract Hilbert space and we givean application for the numerical pricing of Double Barrier Options. In a finitedimension setting, we show the model reduction method for Finite Differenceschemes of implicit type. In particular, we construct the reduced version of theCrank?Nicolson scheme and some numerical examples are give