Implied volatility is an important concept in finance and trading. In this post, I further discuss its breakdown into diffusive volatility and jump risk components.
Decomposing Implied Volatility: Diffusive and Jump Risks
Implied volatility is an estimation of the future volatility of a security’s price. It is calculated using an option-pricing model, such as the Black-Scholes-Merton model.
Reference [1] proposed a method for decomposing implied volatility into two components: a volatility component and a jump component. The volatility component is the price of a portfolio only bearing volatility risks and the jump component is the price of a portfolio only bearing jump risks. The decomposition is made by constructing two option portfolios: a delta- and gamma-neutral but vega-positive portfolio and a delta- and vega-neutral but gamma-positive portfolio. These portfolios bear volatility and jump risks respectively.
Findings
– The study examines the return patterns of straddles and their component portfolios, focusing on jump risk and volatility risk around earnings announcements.
– The findings show that straddle returns closely resemble those of the jump risk portfolio, suggesting that the options market prioritizes earnings jump risk during these events.
– The research highlights the significant role of earnings jump risk in financial markets, as it is substantially priced into straddles and influences both options and stock market behavior.
– A proposed straddle price decomposition method and the S-jump measure could be applied to other market events, such as M & A and natural disasters, to assess risk and pricing dynamics.
This paper discussed an important concept in option pricing theory; that is, the implied volatilities, especially those of short-dated options, comprise not only volatility but also jump risks.
Reference
[1] Chen, Bei and Gan, Quan and Vasquez, Aurelio, Anticipating Jumps: Decomposition of Straddle Price (2022). Journal of Banking and Finance, Volume 149, April 2023, 106755
Measuring Jump Risks in Short-Dated Option Volatility
Unlike long-dated options, short-dated options incorporate not only diffusive volatility but also jump risks. One of the earliest works examining the jump risks is by Carr et al [2].
Reference [3] developed a stochastic jump volatility model that includes jumps in the underlying asset. It then constructed a skew index, a so-called crash index.
Findings
-This paper introduces a novel methodology to measure forward-looking crash risk implied by option prices, using a tractable stochastic volatility jump (SVJ) model.
-The approach isolates the jump size component from the stochastic volatility embedded within uncertainty risk, extending beyond the Black-Scholes-Merton framework.
-The methodology parallels the construction of implied volatility surfaces, enabling the development of an option-implied crash-risk curve (CIX).
-The CIX is strongly correlated with non-parametric option-implied skewness but offers a more refined measure of crash risk by adjusting for stochastic volatility (Vt) and emphasizing tail risk dynamics.
-In contrast, option-implied skewness reflects both crash and stochastic volatility risks, presenting smoother characteristics of the risk-neutral density.
-Empirical analysis reveals a notable upward trend in the CIX after the 2008 financial crisis, aligning with narratives on rare-event risks and emphasizing the value of incorporating such beliefs into asset pricing frameworks.
References
[2] P Carr, L Wu, What type of process underlies options? A simple robust test, The Journal of Finance, 2003
[3] Gao, Junxiong and Pan, Jun, Option-Implied Crash Index, 2024. SSRN
Closing Thoughts
In this issue, I discussed the breakdown of volatility into diffusive and jump components. Understanding this distinction is important for trading, and risk management in theory and practice.