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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. "

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Bibliographic Info

Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 6250.

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Date of creation: Nov 1997
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Publication status: published as Bertsimas, D., L. Kogan, and A. Lo. “Pricing and Hedging Derivative Securities in Incomplete Markets: An ε-Arbitrage approach." Operations Research 49 (2001): 372-397.
Handle: RePEc:nbr:nberwo:6250

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