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50th Anniversary Article
Option Pricing: Valuation Models and Applications
Mark Broadie
Graduate School of Business, Columbia University, 3022 Broadway, New York, New York 10027-6902
Jerome B. Detemple
School of Management, Boston University, 595 Commonwealth Avenue, Boston, Massachusetts 02215
This paper surveys the literature on option pricing from its origins to the present. An extensive review of
valuation methods for European- and American-style claims is provided. Applications to complex securities
and numerical methods are surveyed. Emphasis is placed on recent trends and developments in methodology
and modeling.
Key words: option pricing; American options; risk-neutral valuation; jump and stochastic volatility models
1. Derivatives Markets:
Introduction and Definitions
Management Science has a long tradition of publishing
important research in the finance area, including
significant contributions to portfolio optimization;
asset-liability management; utility theory and stochastic
dominance; and empirical finance and derivative
securities. Within the derivatives area, contributions
in the journal have advanced our understanding of
the pricing, hedging, and risk management of derivative
securities in a wide variety of financial markets,
including equity, fixed income, commodity, and
credit markets. In addition to theoretical advances,
several articles have focused on practical applications
through the design of efficient numerical procedures
for valuing and hedging derivative securities. In this
paper we survey the option pricing literature over
the last four decades, including many articles that
have appeared in the pages of Management Science. We
begin with a description of derivative securities and
their properties.
A derivative security is a financial asset whose payoff
depends on the value of some underlying variable.
The underlying variable can be a traded asset, such
as a stock; an index portfolio; a futures price; a currency;
or some measurable state variable, such as the
temperature at
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