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- Title
HEDGING DERIVATIVE SECURITIES AND INCOMPLETE MARKETS: AN ε-ARBITRAGE APPROACH.
- Authors
Bertsimas, Dimitris; Kogan, Leonid; Lo, Andrew W.
- Abstract
Given a European derivative security with an arbitrary payoff function und 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 ‘∈’ 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, we consider several numerical examples, including path-dependent options and options on assets with stochastic volatility and jumps.
- Subjects
DERIVATIVE securities; SECURITIES; HEDGING (Finance); SELF-financing; INVESTMENTS; ARBITRAGE; DYNAMIC programming
- Publication
Operations Research, 2001, Vol 49, Issue 3, p372
- ISSN
0030-364X
- Publication type
Article
- DOI
10.1287/opre.49.3.372.11218