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

By A. Medvedev, Olivier Scaillet. 2007

118 citations recorded by the source corpus.

We derive a closed-form asymptotic expansion formula for option implied volatility under a two-factor jump-diffusion stochastic volatility model when time-to-maturity is small. Based on numerical experiments we describe the range of time-to-maturity and moneyness for which the approximation is accurate. 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 in order to extract information from the dynamics of the implied volatility smile. An example of calibration to a sample of S&P500 option prices is provided. We find that jumps are significant. The evidence also supports an affine specification for the jump intensity and Constant-Elasticity-of-Variance for the dynamics of the return volatility.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/892e63084aa57d03dc279d2a66a23b78870c7af3

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Citations in the corpus

Consistent Modelling of VIX and Equity Derivatives Using a 3/2 plus Jumps Model (2012, background): “Since this question was answered in Drimus (2012), see his Equation (4), the desired result follows.”
Hermite Polynomial Based Expansion of European Option Prices (2014, unknown): “…expansions, such as those discussed in Hagan and Woodward (1999), Hagan et al. (2002), Fouque et al. (2000), Lewis (2000), Berestycki et al. (2002), Medvedev and Scaillet (2007), Henry-Labordere (2008), Takahashi et al. (2009), Gatheral et al. (2012), Li (2013a, 2013b), Lorig et al. (2013), and…”
Small-Time Asymptotics of Option Prices and First Absolute Moments (2010, background): “Due to their importance for model calibration and testing, small-time asymptotics of option prices have received considerable attention in recent years; see [2, 5, 6, 7, 10, 11, 12, 13, 14, 15, 16, 17, 22, 24].”
ASYMPTOTICS OF IMPLIED VOLATILITY IN LOCAL VOLATILITY MODELS (2012, unknown): “Mathematical Finance, Vol. 22, No. 4 (October 2012), 591–620”
Riding on the smiles (2011, unknown): “( 2009 ) and Bensusan ( 2010 ) we extend to a multi-dimensional framework (both multi-asset and multi-factor) the approach of Lewis ( 2000 ) (see also Medvedev and Scaillet ( 2007 )), based on the characteristic function, which is explicitly known for the affine models.”
Options on realized variance by transform methods: a non-affine stochastic volatility model (2009, unknown): “0: From figure 4 we see very good agreement between the Medvedev and Scaillet (2007) expansion and the true implied volatilities calculated by Fourier inversion.”
Asymptotics for Exponential Levy Processes and Their Volatility Smile: Survey and New Results (2012, background): “, [71], [73], [74], [75], [77], [91], [49], [121], [50].”
Rough volatility: Evidence from option prices (2017, methodology): “In Section 3, instead of using raw implied volatilities, we compute spot volatilities from implied ones through a correction formula due to Medvedev and Scaillet, see [19].”
Short-time at-the-money skew and rough fractional volatility (2015, background): “As already mentioned, (4) partially extends Medvedev and Scaillet (2006) and Osajima (2006).”