Volatility of Volatility as a Risk Factor in Crypto Options

As cryptocurrencies become mainstream, liquidity in crypto derivatives such as perpetual futures and options is improving. They also attract more attention from researchers. Reference [1] contributes to the growing literature on crypto derivatives by studying Bitcoin options volatility. Specifically, it shows that BTC options share both the “usual” and “unusual” volatility components found in traditional finance.

• The usual component reflects volatility evolving gradually in response to macroeconomic developments or regulatory changes.
• The unusual component represents sharp increases in volatility, highlighting heightened volatility of volatility (VOV).

These two characteristics must be incorporated into an options pricing model. The paper proposed a so-called affine realized volatility of volatility (ARVOV) model, which explicitly accounts for VOV risk by introducing a distinct latent variable to capture its dynamics. This latent factor serves as a critical risk driver in the return-generating process and strongly influences volatility behavior.

The authors pointed out,

This paper introduces a novel option pricing framework, the ARVOV model, that explicitly separates the dynamics of volatility and VOV. Distinct from conventional option pricing models, our model treats VOV as an independent source of risk, reflecting uncertainty about future volatility itself, rather than as a mere extension or function of volatility. By incorporating realized VOV measures into the modeling of conditional variance, the ARVOV model offers a more flexible and precise characterization of volatility dynamics in cryptocurrency markets. Utilizing the exponential affine structure of the MGF, we derive a closed‐form European option pricing formula through Fourier inversion. Empirical analyses are conducted using high‐frequency Bitcoin price data and historical Bitcoin options data sourced from Deribit.

Model performance is rigorously evaluated by assessing the RMSE between model‐filtered volatilities and their corresponding realized measures. Additionally, we evaluate option pricing accuracy via the RMSE of implied volatility, defined as the discrepancy between market‐based and model‐based implied volatilities. Empirical results indicate that our ARVOV model reduces implied volatility RMSE by 8.55% compared to the second‐best benchmark. Further robustness tests across various moneyness categories, maturities, and market volatility levels consistently demonstrate the superior performance of the ARVOV model, particularly under conditions of extreme moneyness, shortest and longest maturities, and heightened market volatility.

In short, the study highlights the unique nature of BTC volatility and develops a pricing model that explicitly incorporates VOV risk.

An interesting result is that explicitly modeling VOV allows the variance risk premium (VRP) to take time-varying signs, unlike the predominantly positive VRP found in other studies. This significantly improves the ability to capture the complex behavior of VRP and option prices in highly volatile cryptocurrency markets.

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

References

[1] Lingshan Du, Ji Shen, Pricing Cryptocurrency Options With Volatility of Volatility, Journal of Futures Markets, 2025; 1–26

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