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

64 Pages Posted: 16 Jul 2000 Last revised: 3 Apr 2022

See all articles by Dimitris Bertsimas

Dimitris Bertsimas

Massachusetts Institute of Technology (MIT) - Sloan School of Management

Leonid Kogan

Massachusetts Institute of Technology (MIT) - Sloan School of Management; National Bureau of Economic Research (NBER)

Andrew W. Lo

Massachusetts Institute of Technology (MIT) - Laboratory for Financial Engineering; Santa Fe Institute

Date Written: November 1997

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

Bertsimas, Dimitris and Kogan, Leonid and Lo, Andrew W., Pricing and Hedging Derivative Securities in Incomplete Markets: An E-Aritrage Model (November 1997). NBER Working Paper No. w6250, Available at SSRN: https://ssrn.com/abstract=226008

Dimitris Bertsimas (Contact Author)

Massachusetts Institute of Technology (MIT) - Sloan School of Management ( email )

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Leonid Kogan

Massachusetts Institute of Technology (MIT) - Sloan School of Management ( email )

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HOME PAGE: http://web.mit.edu/lkogan2/www/

National Bureau of Economic Research (NBER)

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Andrew W. Lo

Massachusetts Institute of Technology (MIT) - Laboratory for Financial Engineering ( email )

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HOME PAGE: http://web.mit.edu/alo/www

Santa Fe Institute

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