scholarly journals On the Short-Time Behavior of the Implied Volatility for Jump-Diffusion Models With Stochastic Volatility

2006 ◽  
Author(s):  
Elisa Alos ◽  
Jorge A. Leon ◽  
Josep Vives
Keyword(s):  
Stochastic Volatility ◽  
Implied Volatility ◽  
Jump Diffusion ◽  
Diffusion Models ◽  
Time Behavior ◽  
Short Time

scholarly journals A Hull and White Formula for a General Stochastic Volatility Jump-Diffusion Model with Applications to the Study of the Short-Time Behavior of the Implied Volatility

2008 ◽  
Vol 2008 ◽  
pp. 1-17 ◽  
Author(s):  
Elisa Alòs ◽  
Jorge A. León ◽  
Monique Pontier ◽  
Josep Vives
Keyword(s):  
Stochastic Volatility ◽  
Implied Volatility ◽  
Asset Price ◽  
Jump Diffusion ◽  
Stochastic Volatility Model ◽  
Time Behavior ◽  
Volatility Model ◽  
Jump Diffusion Model ◽  
White Type ◽  
Short Time

We obtain a Hull and White type formula for a general jump-diffusion stochastic volatility model, where the involved stochastic volatility process is correlated not only with the Brownian motion driving the asset price but also with the asset price jumps. Towards this end, we establish an anticipative Itô's formula, using Malliavin calculus techniques for Lévy processes on the canonical space. As an application, we show that the dependence of the volatility process on the asset price jumps has no effect on the short-time behavior of the at-the-money implied volatility skew.

Noise trading and stock market bubbles: what the derivatives market is telling us

2020 ◽  
Vol 46 (9) ◽  
pp. 1165-1182
Author(s):  
Scott B. Beyer ◽  
J. Christopher Hughen ◽  
Robert A. Kunkel
Keyword(s):  
Stochastic Volatility ◽  
Noise Level ◽  
Implied Volatility ◽  
Mean Reversion ◽  
Jump Diffusion ◽  
Futures Prices ◽  
Noise Traders ◽  
Content Type ◽  
Noise Trading ◽  
Technology Bubble

PurposeThe authors examine the relation between noise trading in equity markets and stochastic volatility by estimating a two-factor jump diffusion model. Their analysis shows that contemporaneous price deviations in the derivatives market are statistically significant in explaining movements in index futures prices and option-market volatility measures.Design/methodology/approachTo understand the impact noise may have in the S&P 500 derivatives market, the authors first measure and evaluate the influence noise exerts on futures prices and then investigate its influence on option volatility.FindingsIn the period from 1996 to 2003, this study finds significant changes in the volatility and mean reversion in the noise level and a significant increase in its relation to implied volatility in option prices. The results are consistent with a bubble in technology stocks that occurred with significant increases in noise trading.Research limitations/implicationsThis study provides estimates for this model during the periods preceding and during the technology bubble. The study analysis shows that the volatility and mean reversion in the noise level are much stronger during the bubble period. Furthermore, the relation between noise trading and implied volatility in the futures market was of a significantly larger magnitude during this period. The study results support the importance of noise trading in market bubbles.Practical implicationsBloomfield, O'Hara and Saar (2009) find that noise traders lower bid–ask spreads and improve liquidity through increases in trading volume and market depth. Such improved market conditions could have positive effects on market quality, and this impact could be evidenced by lower implied volatility when noise traders are more active. Indeed, the results in this study indicate that the level and characteristics of noise trading are fundamentally different during the technology bubble, and this noise trading activity has a larger impact during this period on implied volatility in the options market.Originality/valueThis paper uniquely analyzes derivatives on the S&P 500 Index in order to detect the presence and influence of noise traders. The authors derive and implement a two-factor jump diffusion noise model. In their model, noise rectifies the difference of analysts' opinions, market information and beliefs among traders. By incorporating a reduced-form temporal expression of heterogeneities among traders, the model is rich enough to capture salient time-series characteristics of equity prices (i.e. stochastic volatility and jumps). A singular feature of the authors’ model is that stochastic volatility represents the random movements in asset prices that are attributed to nonmarket fundamentals.

The short-time behavior of VIX-implied volatilities in a multifactor stochastic volatility framework

2018 ◽  
Vol 29 (3) ◽  
pp. 928-966 ◽  
Author(s):  
Andrea Barletta ◽  
Elisa Nicolato ◽  
Stefano Pagliarani
Keyword(s):  
Stochastic Volatility ◽  
Time Behavior ◽  
Short Time
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