Pricing and Hedging Derivative Securities in Incomplete Markets: An E-Aritrage Model
Dimitris Bertsimas, Leonid Kogan, Andrew W. Lo
NBER Working Paper No. 6250
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. "
Published: 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.