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

Alexey Medvedev; Olivier Scaillet

doi:10.1093/rfs/hhl013

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

Alexey Medvedev^1,2; Olivier Scaillet^1,2

¹ University of Geneva · ² Swiss Finance Institute

Review of Financial Studies 2007 open access

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.

DOI: 10.1093/rfs/hhl013
Volume: 20 (2)
Pages: 427-459
Language: en
Export: BibTeX
Sources: openalex crossref