Unlike long-dated options, short-dated options incorporate not only diffusive volatility but also jump risks. The commonly used VIX and SKEW indices cannot clearly identify the jump risk component in options volatility. To better isolate and present the jump risk component, Reference [1] developed a stochastic jump volatility model that includes jumps in the underlying asset. The authors pointed out,
In this paper, we have pioneered a methodology to gauge forward-looking crash risk as implied from option prices. Utilizing the tractable SVJ model, this parametric approach isolates the jump size component from the stochastic volatility encapsulated within uncertainty risk. Our method extends beyond the traditional Black-Scholes model, paralleling the construction of the implied volatility surface and facilitating the creation of an option-implied crash-risk curve …
Our method’s efficacy is underscored by its strong correlation with non-parametric option-implied skewness. Nevertheless, we have crafted our CIX as a nuanced measure of crash risk, designed to adjust for the influence of Vt, and illuminate the tail risk aspects of asset pricing dynamics. In juxtaposition, option-implied skewness is reliant on both crash and stochastic volatility risks and epitomizes the more smooth characteristics of the risk-neutral density.
Empirically, we uncover an intriguing upward trend in CIX following the 2008 financial crisis.This finding is well supported by narratives about rare events in news coverage, highlighting the importance of incorporating beliefs about rare events within a theoretical framework.
In short, the author utilized this new framework and calculated a skew index, referred to as a Crash Index, to represent the jump component. This index is highly correlated with the traditional SKEW index, and they also uncovered an interesting upward trend in the Crash Index following the 2008 financial crisis.
This is not the first paper to address jump risks in short-dated options, but its key contribution lies in the construction of a skew index. To the best of our knowledge, one of the earliest works in this area is by Carr et al. [2]
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References
[1] Gao, Junxiong and Pan, Jun, Option-Implied Crash Index (2024). https://ssrn.com/abstract=5035431
[2] P Carr, L Wu, What type of process underlies options? A simple robust test, The Journal of Finance, 2003
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