A Jump Diffusion Model for VIX Volatility Options and Futures

Psychoyios, Dimitris; Dotsis, George; Markellos, Raphael N.

doi:10.2139/ssrn.1136869

Cited by 23 publications

(40 citation statements)

References 26 publications

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“…As indicated in the previous section, model factors such as mean-reversion and jumps are prominent properties of volatility index such as VIX. Psychoyios [13] studies impact of the two properties on fitting VIX historical data by maximum likelihood estimation method, and the paper concludes that MRLRJ serves best under objective measure. Psychoyios [13] then utilizes solely MRLRJ process to model VIX under martingale measure and derives an explicit VIX option pricing formula expressed as the Heston-type formula.…”

Section: Stochastic Volatility-of-volatility Model Of Volatility Indexmentioning

confidence: 99%

“…Psychoyios [13] studies impact of the two properties on fitting VIX historical data by maximum likelihood estimation method, and the paper concludes that MRLRJ serves best under objective measure. Psychoyios [13] then utilizes solely MRLRJ process to model VIX under martingale measure and derives an explicit VIX option pricing formula expressed as the Heston-type formula. Bao [17] conducts a comparative study of Geometric Brownian Motion (GBM), Square-Root (SR), logarithmic (LR) and Mean-Reverting logarithmic jump (MRLRJ) models on fitting VIX options data and generating positive volatility skew and also confirms that MRLRJ is the best candidate for VIX dynamics specification.…”

Section: Stochastic Volatility-of-volatility Model Of Volatility Indexmentioning

confidence: 99%

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Pricing VIX options in a stochastic vol‐of‐vol model

Wang

Huang

et al. 2015

Appl Stoch Models Bus & Ind

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This paper proposes and makes a study of a new model for volatility index option pricing. Factors such as mean-reversion, jumps, and stochastic volatility are taken into consideration. In particular, the positive volatility skew is addressed by the jump and the stochastic volatility of volatility. Daily calibration is used to check whether the model fits market prices and generates positive volatility skews. Overall, the results show that the mean-reverting logarithmic jump and stochastic volatility model (called MRLRJSV in the paper) serves as the best model in all the required aspects.

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Section: Stochastic Volatility-of-volatility Model Of Volatility Indexmentioning

confidence: 99%

Section: Stochastic Volatility-of-volatility Model Of Volatility Indexmentioning

confidence: 99%

Pricing VIX options in a stochastic vol‐of‐vol model

Wang

Huang

et al. 2015

Appl Stoch Models Bus & Ind

View full text Add to dashboard Cite

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“…where θ is the drift term, σ is the volatility of the process, and Table 3 (Cont & Tankov, 2004;Geman, 2002). Psychoyios and Dotsis (2010) compare modeling VIX in the original index level and the logarithm of the original level by using mean-reverting process. Their empirical results conclude that the modeling of VIX with logarithm can improve the goodness-of-fit from modeling of the original level.…”

Section: Infinite-activity Lévy Jump Specificationmentioning

confidence: 99%

“…Thus, different types of mean-reverting processes, such as the squared-root mean-reverting process, the arithmetic mean-reverting process, and the geometric mean-reverting process, are applied for modeling VIX. In addition, Goard and Mazur (2013), Kaeck and Alexander (2013), Mencía and Sentana (2013), and Psychoyios and Dotsis (2010), find clear evidence of jumps in the VIX return process, in which the compound Poisson process is employed to characterize finite-activity jumps triggered by influential financial events. As an advantage, analytical pricing formulae for VIX derivatives can be obtained based on even more complex VIX models.…”

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confidence: 99%

Pricing VIX derivatives with infinite‐activity jumps

Cao

Ruan

et al. 2019

Journal of Futures Markets

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In this paper, we investigate a two-factor VIX model with infinite-activity jumps, which is a more realistic way to reduce errors in pricing VIX derivatives, compared with Mencía and Sentana (2013), J Financ Econ, 108, 367-391. Our two-factor model features central tendency, stochastic volatility and infiniteactivity pure jump Lévy processes which include the variance gamma (VG) and the normal inverse Gaussian (NIG) processes as special cases. We find empirical evidence that the model with infinite-activity jumps is superior to the models with finite-activity jumps, particularly in pricing VIX options. As a result, infinite-activity jumps should not be ignored in pricing VIX derivatives. K E Y W O R D S infinite-activity jumps, maximum log-likelihood estimation, unscented Kalman filter, VIX derivatives J E L C L A S S I F I C A T I O N G12, G13 | INTRODUCTIONTime-varying volatility is a key risk factor in financial markets; thus, understanding the dynamics of volatility variation is crucial for market practitioners and academic researchers. The Chicago Board Options Exchange (CBOE) Volatility Index, known by its ticker symbol VIX, is a risk-neutral gauge of the future implied volatility in the U.S. stock market. It is calculated by the S&P 500 index options market over the next 30-day period and indicates overall stock market fear. 1 VIX can be traded through the VIX derivatives. Because of a negative correlation between the return of VIX and the return of the S&P 500 index, market participants treat the VIX derivatives as an important trading vehicle for reducing exposure to risk. Reported by CBOE, the VIX derivatives include VIX futures and VIX options. In 2004, CBOE introduced VIX futures. According to the CBOE website, the average daily volume of VIX futures rose more than 135fold from 2004 to 2017, with a significant growth after 2010. 2 After the successful launch of VIX futures, CBOE introduced VIX options in 2006, which can provide an alternative way for hedging the market risk with relatively low costs. Since then, the VIX options have become popular financial tools in risk management. Not surprisingly, the average daily volume of VIX options expanded over 28 times between 2006 and 2017. 3 Therefore, it is important to find an accurate valuation model of the VIX derivatives.The methodologies for pricing VIX derivatives can be classified into two directions. In the first direction, the VIX derivatives pricing formulae are derived from the instantaneous volatilities of the S&P 500 index, which can provide a clear picture of the relationship among the S&P 500 index, VIX, and VIX derivatives. Researchers in this direction 1 See https://www.cboe.com/micro/vix/vixwhite.pdf. 2 See http://www.cboe.com/blogs/options-hub/2017/03/01/eight-charts-highlighting-growth-in-options-and-vix-futures. 3 See http://www.cboe.com/blogs/options-hub/2017/08/25/record-days-for-vix-futures-and-options-volume-and-open-interest-this-month.Note: The VG and NIG processes are summarized. The "Parameters" row shows the parameters in t...

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“…3 This study develops a term structure model for VIX futures. Unlike studies to date, which derive the VIX futures price either from a model for the instantaneous variance of the SPX (e.g., Lin, 2007;Lu and Zhu, 2010;Sepp, 2008;Zhang, Shu, & Brenner, 2010;Zhang and Zhu, 2006;Zhu and Zhang, 2007) or a model for the VIX (e.g., Dotsis, Psychoyios, & Skiadopoulus, 2007;Dupoyet, Daigler, & Chen, 2011;Psychoyios, Dotsis, & Markellos, 2010), this study specifies the VIX futures price dynamics exogenously. 4 The empirical features of VIX futures returns (positive skewness, excess kurtosis, and a decreasing volatility term structure for longer term expirations), are captured by assuming that they are normal inverse Gaussian (NIG) distributed and scaled by a volatility function that is dependent on the maturity.…”

Section: Introductionmentioning

confidence: 99%

A Term Structure Model for VIX Futures

Huskaj

Nossman²

2012

Journal of Futures Markets

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This study develops a term structure model for VIX futures. Instead of deriving the VIX futures price from a model for the instantaneous variance of the S&P 500 or a model for the VIX, the VIX futures price dynamics are specified exogenously. The empirical features of VIX futures returns (positive skewness, excess kurtosis, and a decreasing volatility term structure for longer term expirations) are captured by assuming that they are normal inverse Gaussian distributed and scaled by a volatility function that is dependent on the maturity. The usefulness of the resulting model is illustrated in two applications: risk management (via calculating value at risk (VaR)) and asset pricing (via pricing hypothetical VIX options). The results show that the model provides a good fit for the empirical term structure of VIX futures, produces good VaR estimates, and is promising for use in pricing VIX options. C 2012 Wiley Periodicals, Inc. Jrl Fut Mark

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A Jump Diffusion Model for VIX Volatility Options and Futures

Cited by 23 publications

References 26 publications

Pricing VIX options in a stochastic vol‐of‐vol model

Pricing VIX options in a stochastic vol‐of‐vol model

Pricing VIX derivatives with infinite‐activity jumps

A Term Structure Model for VIX Futures

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