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

Medvedev, Alexey; Scaillet, Olivier

doi:10.1093/rfs/hhl013

Cited by 108 publications

(66 citation statements)

References 26 publications

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“…Also, Christoffersen et al (2008, in press) show that two volatility components fit option prices more accurately than one component. 7 Special cases of the general affine jump-diffusions of Duffie et al (2000) are investigated in Bates (1996Bates ( , 2000Bates ( , 2006, Bakshi et al (1997), Andersen et al (2002), Bollerslev and Zhou (2002), Pan (2002), Liu and Pan (2003), Eraker et al (2003), Eraker (2004), Broadie et al (2007) and Medvedev and Scaillet (2007). Processes incorporating jumps that arrive at an infinite rate are covered by Carr and Wu (2004) and Huang and Wu (2004).…”

Section: Risk-neutral Densitiesmentioning

confidence: 99%

A multi-horizon comparison of density forecasts for the S&P 500 using index returns and option prices

Shackleton

Taylor

2010

Journal of Banking & Finance

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a b s t r a c tWe compare density forecasts of the S&P 500 index from 1991 to 2004, obtained from option prices and daily and 5-min index returns. Risk-neutral densities are given by using option prices to estimate diffusion and jump-diffusion processes which incorporate stochastic volatility. Three transformations are then used to obtain real-world densities. These densities are compared with historical densities defined by ARCH models. For horizons of two and four weeks the best forecasts are obtained from risk-transformations of the risk-neutral densities, while the historical forecasts are superior for the one-day horizon; our ranking criterion is the out-of-sample likelihood of observed index levels. Mixtures of the real-world and historical densities have higher likelihoods than both components for short forecast horizons.

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Section: Risk-neutral Densitiesmentioning

confidence: 99%

A multi-horizon comparison of density forecasts for the S&P 500 using index returns and option prices

Shackleton

Taylor

2010

Journal of Banking & Finance

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“…Medvedev and Scaillet (2007) develop similar Taylor expansions for short-term implied volatilities for jump-diffusion stochastic volatility models.…”

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confidence: 99%

Estimation of objective and risk-neutral distributions based on moments of integrated volatility

García

Lewis

Pastorello

et al. 2011

Journal of Econometrics

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a b s t r a c tIn this paper, we present an estimation procedure which uses both option prices and high-frequency spot price feeds to estimate jointly the objective and risk-neutral parameters of stochastic volatility models. The procedure is based on a method of moments that uses analytical expressions for the moments of the integrated volatility and series expansions of option prices and implied volatilities. This results in an easily implementable and rapid estimation technique. An extensive Monte Carlo study compares various procedures and shows the efficiency of our approach. Empirical applications to the Deutsche mark-US dollar exchange rate futures and the S&P 500 index provide evidence that the method delivers results that are in line with the ones obtained in previous studies where much more involved estimation procedures were used.

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“…0 at a fixed strike and are therefore different from those described by Medvedev and Scaillet (2007) for stochastic volatility models with jumps. Indeed, in Medvedev and Scaillet (2007), the expansions are derived for a strike that goes to the initial value of the asset when t goes to 0. The process of the underlying asset is assumed to be a generic positive jump-diffusion and a martingale.…”

Section: Appendix F: Approximation Of Generalized Laplace Distributiomentioning

confidence: 69%

A PDE approach to jump-diffusions

Carr

Cousot

2011

Quantitative Finance

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In this paper, we show that the calibration to an implied volatility surface and the pricing of contingent claims can be as simple in a jump-diffusion framework as in a diffusion framework. Indeed, after defining the jump densities as those of diffusions sampled at independent and exponentially distributed random times, we show that the forward and backward Kolmogorov equations can be transformed into partial differential equations. This enables us to (i) derive Dupire-like equations [Risk Mag., 1994, 7(1), 18-20] for coefficients characterizing these jump-diffusions; (ii) describe sufficient conditions for the processes they induce to be calibrated martingales; and (iii) price path-independent claims using backward partial differential equations. This paper also contains an example of calibration to the S&P 500 market.Martingales, Jump-diffusion processes, Partial differential equations, Calibration, Options,

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

Cited by 108 publications

References 26 publications

A multi-horizon comparison of density forecasts for the S&P 500 using index returns and option prices

A multi-horizon comparison of density forecasts for the S&P 500 using index returns and option prices

Estimation of objective and risk-neutral distributions based on moments of integrated volatility

A PDE approach to jump-diffusions

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