An Approximation Pricing Algorithm in an Incomplete Market: A Differential Geometric Approach
Publication Type
Journal Article
Publication Date
11-2004
Abstract
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.
Keywords
Incomplete markets, asset pricing, Riemannian manifold, cross entropy
Discipline
Finance and Financial Management | Portfolio and Security Analysis
Research Areas
Finance
Publication
Finance and Stochastics
Volume
8
Issue
4
First Page
501
Last Page
523
ISSN
0949-2984
Identifier
10.1007/s00780-004-0128-5
Publisher
Springer Verlag
Citation
Gao, Yuan; Lim, Kian Guan; and Ng, Kah Hwa.
An Approximation Pricing Algorithm in an Incomplete Market: A Differential Geometric Approach. (2004). Finance and Stochastics. 8, (4), 501-523.
Available at: https://ink.library.smu.edu.sg/lkcsb_research/2545