Hedging derivative securities and incomplete markets:: An ε-arbitrage approach
成果类型：
Article
署名作者：
Bertsimas, D; Kogan, L; Lo, AW
署名单位：
Massachusetts Institute of Technology (MIT); University of Pennsylvania
刊物名称：
OPERATIONS RESEARCH
ISSN/ISSBN：
0030-364X
DOI：
10.1287/opre.49.3.372.11218
发表日期：
2001
页码：
372-397
关键词：
摘要：
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.