Breaking Down Volatility: Diffusive vs. Jump Components

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Implied volatility is an important concept in finance and trading. In this issue, I further discuss its breakdown into diffusive volatility and jump risk components and provide a practical example.

In this issue:

• Latest Posts

• Decomposing Implied Volatility: Diffusive and Jump …

  • Findings

• Measuring Jump Risks in Short-Dated Option Volatil …

  • Findings

• Practical Example

• Closing Thoughts

• Educational Video

  • Merton Jump Diffusion model

• Volatility Weekly Recap

• Around the Quantosphere

Latest Posts

• Crypto Market Arbitrage: Profitability and Risk Management (10 min)

• Optimizing Portfolios: Simple vs. Sophisticated Allocation Strategies (10 min)

• Capturing Volatility Risk Premium Using Butterfly Option Strategies (9 min)

• Understanding Mean Reversion to Enhance Portfolio Performance (9 min)

• Volatility Risk Premium: The Growing Importance of Overnight and Intraday Dynamics (12 min)

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

Practical Example

In this post, Kris Abdelmessih provides a concrete example of a straddle trade. In the section "Straddle vs. Vol Thinking," he discusses a concept called the "particle/wave" nature of options. I believe he is referring to the diffusive/jump nature of volatility discussed in this newsletter.

Closing Thoughts

In this issue, I discussed the breakdown of volatility into diffusive and jump components and provided a practical example. Understanding this distinction is important for trading, and risk management in theory and practice.

Educational Video

Merton Jump Diffusion model

This video explains the Merton Jump Diffusion model. The model extends the classic Black-Scholes-Merton framework by incorporating sudden, random jumps in asset prices, capturing the reality that markets don’t always move smoothly. It provides a more realistic way to price options and manage risk in environments where large, unexpected moves occur.

Volatility Weekly Recap

The figure below shows the term structures for the VIX futures (in colour) and the spot VIX (in grey).

U.S. stocks sold off on Friday as hotter-than-expected inflation data, weak consumer sentiment, and Trump’s tariff announcements rattled investors. Major indexes posted weekly losses, with the S&P 500 down 1.5%, its fifth decline in six weeks. The Nasdaq dropped 2.6%, while the Dow lost around 1%. Gold hit a new record, climbing 0.8% to $3,087 per troy ounce. VIX futures stayed in contango throughout the week but flipped to backwardation on Friday. This resulted in returns of 6.9% and 3.21% for VXX and VIXM respectively.

Around the Quantosphere

• Credit quants push strategy that lured trillions in stock market (bnnbloomberg)

• Rebuffed: A Closer Look at Options-Based Strategies (aqr)

• Should Hedge Funds Hedge?: Why Some Alts Should Have a Beta of 1.0 (aqr)

• The Data Wars: Why More Trading Should Mean More Traders (forbes)

• Goldman Sachs attracting female strats with mass meditation (efinancialcareers)

• The Harsh Truth: Retail Investors Take the Brunt of Market Losses (io-fund)

Disclaimer

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