Key takeaways
  • Clustered jumps can flip option skews sign
  • Hawkes jumps let same-sign and opposite-sign moves feed each other
  • Separate upside and downside jump premia
  • BTC jump premia predict futures carry and hedged option results

Bitcoin options do not always behave like a one-way fear gauge. When jumps cluster, the balance between protection and upside bets can shift, and the paper shows that this can make implied volatility skews turn negative or positive. The model uses a bivariate Hawkes process, a jump process in which new jumps can trigger more jumps of the same sign or the opposite sign. That lets returns develop asymmetric, time-varying skewness instead of a fixed pattern. The authors add two jump premia — one for positive jumps and one for negative jumps — so the model can infer how markets price each kind of move from options data. Using Bitcoin options, they show these inferred jump risk premia have predictive power for both the cost of carry in Bitcoin futures and the performance of delta-hedged option strategies. The same framework is meant for markets where sentiment can swing the skew from one side to the other, including cryptocurrencies, meme stocks, G-7 currencies, and some commodities.

Bitcoin daily returns in this sample swung from −30% to 20%. They also came in clumps. That matters because option prices do not just price size. They also price direction. When demand for put protection rises, the skew tilts negative. When traders chase upside, it can tilt positive. This model says both moods can live in the same market. It treats jumps like sparks that can light more sparks. And it lets the skew turn over when sentiment turns. If you trade crypto, or even just watch it, that is the surprise. Bitcoin options are not stuck as one-way fear gauges.

Why the skew can flip

The sample runs from April 2019 to May 2024. Figure 1 tracks daily BTC returns, at-the-money implied volatility, and call and put skews. At-the-money means options priced near the market level. The chart shows huge moves. It also shows clustering. The skew flips from negative to positive. That happens when fear demand fades and upside demand takes over. A bivariate Hawkes process captures this pattern. It uses two linked jump streams. One stream handles positive jumps. The other handles negative jumps. Each jump can pull more jumps of the same sign. That is self-excitation. A jump can also stir the other stream. That is cross-excitation. The model then prices those jumps with two jump premia. One premium covers positive jumps. The other covers negative jumps. Those premia let options reveal how the market values each kind of jump.

How the jump model remembers shocks

A Hawkes process is a jump model that remembers shocks. A bivariate version tracks two streams at once. Here, those streams split into positive and negative jumps. Each new jump can raise the odds of another jump. That is the self-excitation part. One sign can also wake up the other sign. That is cross-excitation. The option model then adds two jump premia. A premium is the extra price traders pay for jump risk. One premium prices upside jumps. The other prices downside jumps. That split gives the model room to fit sign changes in skew.

−30% to 20%daily BTC return swings

April 2019–May 2024

  1. Positive jumps can trigger more positive jumps.
  2. Negative jumps can trigger more negative jumps.
  3. A jump can also wake up the opposite sign.
  4. Options can price upside and downside jump risk separately.

“This feature is especially relevant for assets such as cryptocurrencies, so-called “meme” stocks, G-7 currencies, and certain commodities, where implied volatility skews may change sign depending on prevailing sentiment.”

From the abstract

“implied volatility skews may change sign”

Why Bitcoin futures and hedged trades care

These jump premia do more than fit charts. In BTC options, they help predict the cost of carry in futures. Cost of carry is the gap between buying now and buying later. They also help predict how delta-hedged option strategies perform. Delta-hedged means you keep adjusting the coin position as prices move. That makes the option bet less sensitive to small price swings. Traders use that setup for both hedging and speculation. A model that splits upside and downside jump risk gives a clearer map. It shows which kind of jump the market fears or welcomes. It also fits markets where sentiment can flip fast. Crypto, meme stocks, G-7 currencies, and some commodities sit in that group.

What to watch next

The next test is whether this sign-flip story holds beyond BTC. The abstract names meme stocks, G-7 currencies, and certain commodities. Those markets can swing from panic to chase. If the model works there too, upside jump risk and downside jump risk become separate line items. That would make skew feel less like a fixed badge of fear. It would make it look more like a live read on crowd mood. The surprise stays the same. Clustered jumps do not just pile up. They can also flip the market's tilt.