Standard Article

Econometrics of Option Pricing

  1. Eric Renault

Published Online: 15 MAY 2010

DOI: 10.1002/9780470061602.eqf19001

Encyclopedia of Quantitative Finance

Encyclopedia of Quantitative Finance

How to Cite

Renault, E. 2010. Econometrics of Option Pricing. Encyclopedia of Quantitative Finance. .

Author Information

  1. University of North Carolina at Chapel Hill, Chapel Hill, NC, USA

Publication History

  1. Published Online: 15 MAY 2010

Abstract

The information content of a cross-section of European option prices written on a given stock with a given time to maturity is summarized by the volatility smile. This article discusses how to graph the volatility smile, to interpret its asymmetry, convexity, term structure and time variation. Implied volatility, implied risk aversion, risk neutral valuation, and pricing kernels are discussed in the context of dynamic mixtures of geometric Brownian motions, possibly featuring stochastic volatility, long range dependence in volatility, and Poisson jumps. More general stochastic processes with possibly infinite activity jump processes as well as more data-driven nonparametric approaches are also sketched.

Keywords:

  • option pricing;
  • volatility smile;
  • moneyness;
  • stochastic volatility;
  • pricing kernel;
  • geometric Brownian motion;
  • mixtures;
  • jumps;
  • risk neutral valuation