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RFS Advance Access originally published online on June 30, 2006
Review of Financial Studies 2007 20(2):427-459; doi:10.1093/rfs/hhl013
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© The Author 2006. Published by Oxford University Press on behalf of The Society for Financial Studies. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org.

Approximation and Calibration of Short-Term Implied Volatilities Under Jump-Diffusion Stochastic Volatility

Alexey Medvedev
HEC Genève and Swiss Finance Institute, Université de Genève

Olivier Scaillet
HEC Genève and Swiss Finance Institute, Université de Genève

Address correspondence to Olivier Scaillet, Université de Genève, UNI MAIL, Faculté des SES, 102 Bd Carl Vogt, 1211 Geneva 4, Switzerland, or e-mail: scaillet{at}hec.unige.ch.


  Abstract

We derive an asymptotic expansion formula for option implied volatility under a two-factor jump-diffusion stochastic volatility model when time-to-maturity is small. We further propose a simple calibration procedure of an arbitrary parametric model to short-term near-the-money implied volatilities. An important advantage of our approximation is that it is free of the unobserved spot volatility. Therefore, the model can be calibrated on option data pooled across different calendar dates to extract information from the dynamics of the implied volatility smile. An example of calibration to a sample of S&P 500 option prices is provided. (JEL G12)


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