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

Yuan Gao (), Kian Lim () and Kah Ng

Finance and Stochastics, 2004, vol. 8, issue 4, 523 pages

Abstract: 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 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. Copyright Springer-Verlag Berlin/Heidelberg 2004

Keywords: Incomplete markets; asset pricing; Riemannian manifold; cross entropy (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1007/s00780-004-0128-5

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