Approximation and Calibration of Short-Term Implied Volatilities under Jump-Diffusion Stochastic Volatility
AbstractWe 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.
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Bibliographic InfoPaper provided by Swiss Finance Institute in its series Swiss Finance Institute Research Paper Series with number 06-08.
Length: 42 pages
Date of creation:
Date of revision: Jan 2006
Option pricing; stochastic volatility; asymptotic approximation; jump-diffusion;
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- Jan Baldeaux & Alexander Badran, 2012.
"Consistent Modeling of VIX and Equity Derivatives Using a 3/2 plus Jumps Model,"
1203.5903, arXiv.org, revised Aug 2012.
- Jan Baldeaux & Alexander Badran, 2012. "Consistent Modeling of VIX and Equity Derivatives Using a 3/2 plus Jumps Model," Research Paper Series 306, Quantitative Finance Research Centre, University of Technology, Sydney.
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- Elisa Alòs & Jorge León & Josep Vives, 2007. "On the short-time behavior of the implied volatility for jump-diffusion models with stochastic volatility," Finance and Stochastics, Springer, vol. 11(4), pages 571-589, October.
- Elisa Alòs & Jorge A. León, 2013. "On the closed-form approximation of short-time random strike options," Economics Working Papers 1347, Department of Economics and Business, Universitat Pompeu Fabra.
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