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Pricing and Hedging Derivative Securities in Incomplete Markets: An E-Aritrage Model

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  • Dimitris Bertsimas
  • Leonid Kogan
  • Andrew W. Lo

Abstract

Given a European derivative security with an arbitrary payoff function and a corresponding set of" underlying securities on which the derivative security is based, we solve the dynamic replication problem: find a" self-financing dynamic portfolio strategy involving only the underlying securities that most closely" approximates the payoff function at maturity. By applying stochastic dynamic programming to the minimization of a" mean-squared-error loss function under Markov state-dynamics, we derive recursive expressions for the optimal-replication strategy that are readily implemented in practice. The approximation error or " " of the optimal-replication strategy is also given recursively and may be used to quantify the "degree" of market incompleteness. " To investigate the practical significance of these -arbitrage strategies examples including path-dependent options and options on assets with stochastic volatility and jumps. "

Suggested Citation

  • Dimitris Bertsimas & Leonid Kogan & Andrew W. Lo, 1997. "Pricing and Hedging Derivative Securities in Incomplete Markets: An E-Aritrage Model," NBER Working Papers 6250, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:6250
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    References listed on IDEAS

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    Cited by:

    1. Elyes Jouini & Pierre-Francois Koehl, "undated". "Pricing of Non-redundant Derivatives in a Complete Market," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-009, New York University, Leonard N. Stern School of Business-.
    2. Dimitris Bertsimas & Leonid Kogan & Andrew W. Lo, 2001. "When Is Time Continuous?," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar(Volume II), chapter 3, pages 71-102, World Scientific Publishing Co. Pte. Ltd..
    3. Merton, Robert C, 1998. "Applications of Option-Pricing Theory: Twenty-Five Years Later," American Economic Review, American Economic Association, vol. 88(3), pages 323-349, June.
    4. D. G. Luenberger, 2004. "Pricing a Nontradeable Asset and Its Derivatives," Journal of Optimization Theory and Applications, Springer, vol. 121(3), pages 465-487, June.
    5. Sanjiv Ranjan Das & Rangarajan K. Sundaram, 2002. "An approximation algorithm for optimal consumption/investment problems," Intelligent Systems in Accounting, Finance and Management, John Wiley & Sons, Ltd., vol. 11(2), pages 55-69, April.
    6. Peter Ryan, 2000. "Tighter Option Bounds from Multiple Exercise Prices," Review of Derivatives Research, Springer, vol. 4(2), pages 155-188, May.

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    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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