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English

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

Published inThe Review of financial studies, vol. 20, no. 2, p. 427-459
Publication date2007
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.

Keywords
  • Option pricing
  • Stochastic volatility
  • Asymptotic approximation
  • Jump-diffusion
Citation (ISO format)
MEDVEDEV, Alexey, SCAILLET, Olivier. Approximation and Calibration of Short-Term Implied Volatilities Under Jump-Diffusion Stochastic Volatility. In: The Review of financial studies, 2007, vol. 20, n° 2, p. 427–459. doi: 10.1093/rfs/hhl013
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ISSN of the journal0893-9454
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