Stochastic Models of Implied Volatility Surfaces

16 Pages Posted: 28 Apr 2003

See all articles by Rama Cont

Rama Cont

University of Oxford

Valdo Durrleman

Princeton University - Department of Operations Research and Financial Engineering

José Da Fonseca

Auckland University of Technology - Faculty of Business & Law

Abstract

We propose a market-based approach to the modelling of implied volatility, in which the implied volatility surface is directly used as the state variable to describe the joint evolution of market prices of options and their underlying asset. We model the evolution of an implied volatility surface by representing it as a randomly fluctuating surface driven by a finite number of orthogonal random factors. Our approach is based on a Karhunen-Loeve decomposition of the daily variations of implied volatilities obtained from market data on SP500 and DAX options.

We illustrate how this approach extends and improves the accuracy of the well-known 'sticky moneyness' rule used by option traders for updating implied volatilities. Our approach gives a justification for the use of 'Vegas' for measuring volatility risk and provides a decomposition of volatility risk as a sum of independent contributions from empirically identifiable factors.

Keywords: Implied volatility, volatility risk, risk management, portfolios of options

JEL Classification: G130, C14, C31

Suggested Citation

Cont, Rama and Durrleman, Valdo and Da Fonseca, José, Stochastic Models of Implied Volatility Surfaces. Economic Notes, Vol. 31, No. 2, July 2002. Available at SSRN: https://ssrn.com/abstract=317604 or http://dx.doi.org/10.2139/ssrn.317604

Rama Cont (Contact Author)

University of Oxford ( email )

Mathematical Institute
Oxford, OX2 6GG
United Kingdom

HOME PAGE: http://https://www.maths.ox.ac.uk/people/rama.cont

Valdo Durrleman

Princeton University - Department of Operations Research and Financial Engineering ( email )

Princeton, NJ 08544
United States

José Da Fonseca

Auckland University of Technology - Faculty of Business & Law ( email )

3 Wakefield Street
Private Bag 92006
Auckland Central 1020
New Zealand
64 9 921 9999 5063 (Phone)

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