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

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

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...

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Bibliographic Details
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
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Institution: Singapore Management University
Language: English
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Summary: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.

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