Hedging Derivative Securities and Incomplete Markets: An (epsilon)-Arbitrage Approach

Dimitris Bertsimas (), Leonid Kogan and Andrew Lo ()
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Dimitris Bertsimas: MIT Sloan School of Management, 50 Memorial Drive, Cambridge, Massachusetts 02142-1347

Operations Research, 2001, vol. 49, issue 3, 372-397

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 optimal-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 “(epsilon)” 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 (epsilon)-arbitrage strategies, we consider several numerical examples, including path-dependent options and options on assets with stochastic volatility and jumps.

Keywords: Finance: derivatives; pricing; and hedging; Dynamic programming/optimal control: stochastic optimization of hedging errors (search for similar items in EconPapers)
Date: 2001
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Citations: View citations in EconPapers (34)

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