Expected gain-loss pricing and hedging of contingent claims in incomplete markets by linear programming

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Pinar M. C., Salih A., Camci A.

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, vol.201, no.3, pp.770-785, 2010 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 201 Issue: 3
  • Publication Date: 2010
  • Doi Number: 10.1016/j.ejor.2009.02.031
  • Journal Name: EUROPEAN JOURNAL OF OPERATIONAL RESEARCH
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Social Sciences Citation Index (SSCI), Scopus
  • Page Numbers: pp.770-785
  • Keywords: Contingent claim, Pricing, Hedging, Martingales, Stochastic linear programming, Transaction costs, SECURITIES MARKETS, PROSPECT-THEORY, ARBITRAGE, MARTINGALES, BOUNDS, COSTS, RISK
  • TED University Affiliated: No

Abstract

We analyze the problem of pricing and hedging contingent claims in the multi-period, discrete time, discrete state case using the concept of a "lambda gain-loss ratio opportunity". Pricing results somewhat different from, but reminiscent of, the arbitrage pricing theorems of mathematical finance are obtained. Our analysis provides tighter price bounds on the contingent claim in an incomplete market, which may converge to a unique price for a specific value of a gain-loss preference parameter imposed by the market while the hedging policies may be different for different sides of the same trade. The results are obtained in the simpler framework of stochastic linear programming in a multi-period setting. and have the appealing feature of being very simple to derive and to articulate even for the non-specialist. They also extend to markets with transaction costs. (C) 2009 Elsevier B.V. All rights reserved.