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Private Valuation of Contingent Claims in a Discrete Time/State Model

  • Alan J. King
  • Olga Streltchenko
  • Yelena Yesha

Abstract

The importance of the risk-neutral measure as a pricing operator generates interest in the calibration problem: given observed market prices, retrieve a pricing measure compatible with them. It can be established through convex duality arguments that the Arbitrage Pricing Theory calibration problem, i.e., calibration to a set of benchmark securities, is equivalent to a certain portfolio optimization problem. We present an explicit duality argument to extend this result: every portfolio optimization problem in a market that allows liquid trading is equivalent to a pricing measure retrieval problem, and vice versa. The resulting pricing measures reflect private valuation of investors’ positions – a consequence of considering portfolio optimization problem from the point of view of a hedger endowed with specific goals and liabilities. Such an investor operates in a “submarket” of available financial securities, which he must see as arbitrage-free, but in which he may be a buyer or seller of particular contingent claims depending on his particular liabilities and goals. This perspective shifts our vision of arbitrage pricing from a “global” to a “local” market, i.e., to the one seen by an investor through the prism of his particular portfolio. It also allows us to use microeconomic considerations when choosing a calibration utility.

Keywords

Relative Entropy Portfolio Optimization Contingent Claim Relative Risk Aversion Terminal Wealth 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Alan J. King
    • 1
  • Olga Streltchenko
    • 2
  • Yelena Yesha
    • 3
  1. 1.IBM Research, Yorktown HeightsNew YorkUSA
  2. 2.Bank of MontrealOntarioUSA
  3. 3.University of MarylandBaltimore CountyUSA

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