Premium
Monte Carlo valuation of American options
Author(s) -
Rogers L. C. G.
Publication year - 2002
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/1467-9965.02010
Subject(s) - martingale (probability theory) , stochastic game , valuation (finance) , martingale pricing , upper and lower bounds , monte carlo method , mathematical economics , economics , local martingale , lagrangian , mathematics , mathematical optimization , econometrics , valuation of options , risk neutral measure , finance , mathematical analysis , statistics
This paper introduces a dual way to price American options, based on simulating the paths of the option payoff, and of a judiciously chosen Lagrangian martingale. Taking the pathwise maximum of the payoff less the martingale provides an upper bound for the price of the option, and this bound is sharp for the optimal choice of Lagrangian martingale. As a first exploration of this method, four examples are investigated numerically; the accuracy achieved with even very simple choices of Lagrangian martingale is surprising. The method also leads naturally to candidate hedging policies for the option, and estimates of the risk involved in using them.