How Bitcoin Options Compare to Equity Index Options: Volatility, Correlation, and Skew

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Bitcoin options are derivative contracts that grant investors the right, but not the obligation, to buy or sell Bitcoin at a predetermined price before a specified expiration date. Major cryptocurrency exchanges offer options on Bitcoin and other cryptocurrencies, including select tokens. However, the vast majority of trading takes place on the Deribit options exchange, which alone accounts for over 90% of Bitcoin options trading volume.

With the growing popularity of Bitcoin options, an important question arises: how do Bitcoin options’ volatility dynamics behave?

Reference [1] explores this issue. The study first highlights a key difference between Bitcoin and equity markets: in traditional stock markets, volatility tends to decline when stock indices rise. In contrast, cryptocurrency volatility can increase regardless of whether prices are moving up or down. This characteristic is reflected in the dynamics of Bitcoin’s volatility surface.

The article further compares the equity index and Bitcoin options.

• In equity markets, the correlation between an index’s price and its implied volatility is typically large and negative. However, for Bitcoin, this correlation appears to be regime-dependent. From August 2019 to November 2020, the correlation between Bitcoin’s price and its 30-day ATM implied volatility was approximately -0.42. During the following five months, it rose sharply to 0.74, and between July and November 2022, the correlation was nearly neutral at 0.08.
• In traditional equity markets, the pronounced and nearly linear skew of the implied volatility curve means that the options that increase the most in price following a market downturn are those with the lowest moneyness. By contrast, Bitcoin’s implied volatility curve was relatively symmetric before the crash on March 12, 2020. At that time, ATM options had the lowest volatility, around 50%, while both OTM puts and calls had roughly equal but higher volatilities of approximately 75% for moneyness levels of 0.7 and 1.3.
• However, a clear asymmetry in the volatility smile emerged after the crash, as risk-averse investors sought protection against another significant price drop. The implied volatility of 30-day deep OTM puts surged to nearly 200%. For the first time, Bitcoin exhibited a pronounced negative skew, though the skew remained flatter than what is typically observed in equity index options.

Despite these differences, Bitcoin’s implied volatility dynamics do share some similarities with equity index options.

• First, volatilities at different moneyness levels tend to move in tandem with ATM volatility of the same maturity, showing a high degree of correlation.
• Second, Bitcoin’s implied volatility term structure exhibits cycles of backwardation during high-volatility periods and contango during relatively calm market conditions. Bitcoin’s implied volatilities tend to move in sync, with minimal dispersion, throughout most backwardation periods, similar to equity index volatility term structures.

This article provides valuable insights for investors, portfolio managers, and market makers in the Bitcoin options market, offering a deeper understanding of its volatility patterns and risk dynamics.

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

References

[1] Alexander, C., & Imeraj, A. (2023). Delta hedging bitcoin options with a smile. Quantitative Finance, 23(5), 799–817.

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