Continuous-time VIX dynamics: On the role of stochastic volatility of volatility

Kaeck, Andreas; Alexander, Carol

doi:10.1016/j.irfa.2013.01.008

Cited by 45 publications

(53 citation statements)

References 28 publications

(1 reference statement)

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“…In this case, there are usually two ways to deal with the dynamics of VIX: affine and non-affine (see e.g. Mencia and Sentana (2013), Kaeck and Alexander (2013), Goard and Mazur (2013)). In the catalogue of non-affine models, modelling logarithm of VIX directly is most popular and has been proved empirically better than affine assumption of VIX.…”

Section: Literature Reviewmentioning

confidence: 99%

“…In that paper, they first put forward the stochastic volatility of volatility model of VIX and model the volatility factor using pure jump OU process. Kaeck and Alexander (2013) employ VIX data of nearly 20 years to estimate the VIX models with and without stochastic volatility using MCMC method. They model the volatility factor as a square-root diffusion process and prove the stochastic volatility model fits better for the VIX historical data.…”

Section: Literature Reviewmentioning

confidence: 99%

“…In Kaeck and Alexander (2013), they put forward a stochastic volatility of volatility model for VIX. They assume the logarithm of VIX has a normal jump while its stochastic volatility factor satisfies a square-root diffusion model.…”

Section: A Motivationmentioning

confidence: 99%

“…Jumps in VIX are also added by some authors. Recently, a novel parameterized stochastic volatility model for VIX is put forward by Mencia and Sentana (2013) and Kaeck and Alexander (2013). They specify a new process to model the volatility of VIX which may be correlated with VIX and show its empirical advantage over the other traditional models.…”

Section: Introductionmentioning

confidence: 99%

“…However, the model specification of this novel stochastic volatility diverges between them. Mencia and Sentana (2013) adopt a pure-jump OU process out of the analytical treatability while Kaeck and Alexander (2013) characterize the volatility as a square root diffusion which takes the correlation of the volatility and VIX into account. How to specify and estimate this volatility factor and further interpret the dynamics of VIX better is still an open problem.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Double-Jump Stochastic Volatility Model for VIX: Evidence from VVIX

Zang

Huang

et al. 2015

SSRN Journal

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The paper studies the continuous-time dynamics of VIX with stochastic volatility and jumps in VIX and volatility. Built on the general parametric affine model with stochastic volatility and jump in logarithm of VIX, we derive a linear relation between the stochastic volatility factor and VVIX index. We detect the existence of co-jump of VIX and VVIX and put forward a double-jump stochastic volatility model for VIX through its joint property with VVIX. With VVIX index as a proxy for the stochastic volatility, we use MCMC method to estimate the dynamics of VIX. Comparing nested models on VIX, we show the jump in VIX and the volatility factor is statistically significant. The jump intensity is also statedependent. We analyze the impact of jump factor on the VIX dynamics.

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Section: Literature Reviewmentioning

confidence: 99%

Section: Literature Reviewmentioning

confidence: 99%

Section: A Motivationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Double-Jump Stochastic Volatility Model for VIX: Evidence from VVIX

Zang

Huang

et al. 2015

SSRN Journal

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The mean‐reverting 4/2 stochastic volatility model: Properties and financial applications

Escobar‐Anel

Gong

2020

Appl Stoch Models Bus & Ind

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This article defines and studies a stochastic process that combines two important stylized facts of financial data: reversion to the mean, and a flexible generalized stochastic volatility process: the 4/2 process. This work is motivated by the modeling of at least two financial asset classes: commodities and volatility indexes. We provide analytical expressions for the conditional characteristic functions and closed-form approximations to relevant cases, in particular a mean-reverting Heston stochastic volatility model. Our results describe feasible changes of measure with the final aim of pricing financial derivatives. The empirical analysis and the estimation methodology confirm the need of such a model in several examples from the targeted asset classes. Applications to option pricing corroborate the substantial impact on the implied volatility surfaces of the new parameters.

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Instantaneous squared VIX and VIX derivatives

Luo

Zhang

2019

Journal of Futures Markets

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In this paper, we propose a parsimonious and efficient model to price derivatives written on VIXs with different horizons. Our model is built on Luo and Zhang's (2012, J Futures Markets, 32, 1092–1123) concept of the instantaneous squared VIX (ISVIX) that is the sum of instantaneous diffusive and jump variances of the SPX return. Modeling the ISVIX as a mean‐reverting jump‐diffusion process with a stochastic long‐term mean, we obtain analytical formulas for VIX options and futures. Estimation with VIX term structure and calibration with VIX options data show that our model performs well in matching both time series and cross‐sectional VIX derivatives market prices.

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Continuous-time VIX dynamics: On the role of stochastic volatility of volatility

Cited by 45 publications

References 28 publications

Double-Jump Stochastic Volatility Model for VIX: Evidence from VVIX

Double-Jump Stochastic Volatility Model for VIX: Evidence from VVIX

The mean‐reverting 4/2 stochastic volatility model: Properties and financial applications

Instantaneous squared VIX and VIX derivatives

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