TY - JOUR
AU - Bertsimas, Dimitris
AU - Kogan, Leonid
AU - Lo, Andrew W
TI - Pricing and Hedging Derivative Securities in Incomplete Markets: An E-Aritrage Model
JF - National Bureau of Economic Research Working Paper Series
VL - No. 6250
PY - 1997
Y2 - November 1997
DO - 10.3386/w6250
UR - http://www.nber.org/papers/w6250
L1 - http://www.nber.org/papers/w6250.pdf
N1 - Author contact info:
Leonid Kogan
MIT Sloan School of Management
100 Main Street, E62-636
Cambridge, MA 02142
Tel: 617/504-9728
Fax: 617/258-6855
E-Mail: lkogan@mit.edu
Andrew W. Lo
MIT Sloan School of Management
100 Main Street, E62-618
Cambridge, MA 02142
Tel: 617/253-0920
Fax: 781/891-9783
E-Mail: alo-admin@mit.edu
AB - 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. "
ER -