Derivatives Valuation Based on Arbitrage: The Trade is Crucial

• Published date: 01 April 2017
• Author: Stephen Figlewski
• DOI: http://doi.org/10.1002/fut.21806
• Date: 01 April 2017

Derivatives Valuation Based on Arbitrage:

The Trade is Crucial

Stephen Figlewski*

Derivatives valuation has strong theoretical support because models are derived from the

principle that arbitrage be tween the derivative and its und erlying will eliminate risk less

profits and drive the market price to the model value. “No-arbitrage”is invoked routinely

whenever a new pricing model is developed. But real world market prices are determined by

trades, not by theories. In this talk, I discusshow different the arbitrage trade is for different

markets and different model s and I review articles from th e literature that illustra te how

limits to the arbitrage trade have affected the way derivatives theory gets into prices in

practice. © 2016 Wiley Periodi cals, Inc. Jrl Fut Mark 37:316–327 , 2017

1. INTRODUCTION

It is an honor and a pleasure to have this opportunity to discuss with you today one of the

major themes that has motivated my research over the last 40 years. It also allows me to

shamelessly promote a number of my earlier papers as I describe the evolution of these ideas

through a series of articles that all focus on arbitrage, the trade that connects our theoretical

derivatives valuation models to the real world markets for futures, options and other

contingent claims.

Arbitrage, or more precisely, the lack of profitable arbitrage opportunities, is what drives

our pricing models. Derivatives theory is based on the principle that when the same payoff

can be produced in two or more different ways in the market, arbitrage (true arbitrage!) must

force them all to be priced exactly the same. In theoretical modeling, this is often summarized

in the shorthand expression: “We assume no-arbitrage,”meaning that prices within the

model allow no possibility of profitable riskless arbitrage. Since theoretical model values are

derived from riskless positions, they do not depend on how risk averse traders are. Models that

satisfy no-arbitrage exhibit the extremely useful property of “risk-neutral”pricing.

In theoretical modeling, no-arbitrage is a mathematical condition that the model

specification must satisfy. If there are two ways to achieve exactly the same payoff on a given

future date (e.g., futures expiration), but they have different costs today, an arbitrageur buys

the cheaper position and sells (short) the higher priced one. This trade locks in the initial

price difference as a riskless profit. Because everyone would like to make free money with no

risk, the forces to eliminate arbitrage opportunities are very strong, even if there are only a

Stephen Figlewski is Professor of Finance at New York University Stern School of Business, New York, New

York. I thank the participants at the 2016 China Derivatives Markets Conference for their feedback on the

ideas presented here. Financial support from the NASDAQ Educational Foundation is gratefully

acknowledged.

*Correspondence author, New York University Stern School of Business, 44 West 4th Street, Suite 9-160, New

York, NY 10012-1126. Tel: 212-998-0712, Fax: 212-995-4220, e-mail: sfiglews@stern.nyu.edu

Received June 2016; Accepted July 2016

The Journal of Futures Markets, Vol. 37, No. 4, 316–327 (2017)

© 2016 Wiley Periodicals, Inc.

Published online 7 September 2016 in Wiley Online Library (wileyonlinelibrary.com).

DOI: 10.1002/fut.21806