An Approximation Pricing Algorithm in an Incomplete Market: A Differential Geometric Approach

• Main Authors: Gao, Yuan, Lim, Kian Guan, Ng, Kah Hwa
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2004
• Subjects: Incomplete markets; asset pricing; Riemannian manifold; cross entropy; Finance and Financial Management; Portfolio and Security Analysis
• Online Access: https://ink.library.smu.edu.sg/lkcsb_research/2545; https://search.ebscohost.com/login.aspx?direct=true&db=buh&AN=14442764&site=ehost-live
• Institution: Singapore Management University

The minimal distance equivalent martingale measure (EMM) defined in Goll and Rⁿschendorf (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 shown on the manifold. An optimization algorithm on the Riemannian manifold becomes the approximation pricing algorithm. The financial interpretation of the geometry is also given in terms of pricing model risk.