Diffusive Volatility and Jump Risks

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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 model, as it takes into account various factors including the current price of the underlying asset and its strike price. Implied volatility helps investors to gauge how volatile a stock or other security might be in the future, and can be used to inform trading decisions. It is not a static figure; rather it changes over time as market conditions change or new information is released.

Implied volatility actually consists of two parts,

  • Diffusive volatility, and
  • Jump-related volatility

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.

The authors pointed out,

We analyze the return pattern of straddles and their component portfolios, jump risk and volatility risk, around earnings announcements. We find that straddle returns and the jump risk portfolio returns behave similarly. We argue that the options market places more emphasis on earnings jump risk around earnings announcements…

Our study confirms the important role played by earnings jump risk in financial markets. Earnings jump risk is substantially priced in straddles and strongly influences the behavior of the options and stock markets. Our straddle price decomposition method and the S-jump measure could also be used in other events, such as M&A and natural disasters.

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.

Let us know what you think in the comments below or in the discussion forum.

References

[1] Chen, Bei and Gan, Quan and Vasquez, Aurelio, Anticipating Jumps: Decomposition of Straddle Price (2022). Journal of Banking and Finance, Forthcoming

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