An approximation pricing algorithm in an incomplete market: A differential geometric approach

The minimal distance equivalent martingale measure (EMM) defined in Goll and Rüschendorf (2001) is the arbitrage-free equilibrium pricing measure. This paper provides an algorithm to approximate its density and the fair price of any contingent claim in an incomplete market. We first approximate the infinite dimensional space of all EMMs by a finite dimensional manifold of EMMs. A Riemannian geometric structure is then shown on the manifold. An optimization algorithm on the Rieman? Present address: Center for Financial Engineering, National University of Singapore, 12 Prince George’s Park, Singapore 118411. Fax: (065)68745430. 2 Yuan Gao et al. nian manifold becomes the approximation pricing algorithm. The financial interpretation of the geometry is also given in terms of pricing model risk.