Bitcoin's (BTC) recent double-digit rally has sparked a positive sentiment shift among crypto options traders.

The leading cryptocurrency by market value has gained 13% this month, topping the $19,000 mark for the first time since Nov. 8, CoinDesk data show.

Tumbling U.S. inflation, weaker U.S. dollar, and expectations for slower Federal Reserve rate hikes have helped the cryptocurrency look past the lingering fallout from FTX's collapse.

And consistent with the resilient rally, bitcoin options' "volatility smile" shows the demand for out-of-the-money (OTM) call options – bullish bets at strikes higher than the cryptocurrency's going market price – has increased relative to puts or bearish bets.

"BTC's short-dated OTM calls have seen an increase in implied volatility compared to OTM puts. This continues the trend of the volatility smile towards a more neutral smile, which was previously driven by a falling demand for downside protection [puts] throughout December," Andrew Melville, research analyst at crypto derivatives analytics firm Block Scholes, wrote in a note published Thursday.

"It indicates that BTC's derivatives market is now not only pricing for a drop in bearish sentiment but is reflecting an increase in demand for exposure to upwards movements," Melville added.

The bullish shift perhaps reflects confidence among sophisticated market participants that bitcoin's rally to two-month highs may be only the first milestone in its upward trajectory.

The volatile smile is a graphical representation of implied volatility for a series of bullish call and bearish put options at different strikes but with the same underlying and expiration date. Implied volatility (IV) or projected volatility is the market's expectation of the future price turbulence of the underlying asset and is directly influenced by supply and demand for call and put options.

A U-shaped line is formed sloping upwards on both ends, which resembles a smile, when IVs for options at different strike prices are plotted. The simplest explanation for the U-shape is demand for out-of-the-money (OTM) and in-the-money (ITM) call and put options is typically higher than for at-the-money (ATM) call and put options, as Patrick Boyle and Jesse McDougall wrote in the book "Trading and Pricing Financial Derivatives."

Call options above BTC's going market price, currently $18,850, are known as OTM, while those below the spot price are ITM. The opposite is the case for puts, with options above the spot price known as ITM while those below called OTM. Call and put options at strikes at around the spot price are ATM options.

Bitcoin's volatility smile

The chart by Block Scholes shows bitcoin's 30-day volatility smile on Dec. 5 (blue line), Jan. 6 (grey line) and Jan. 12 (yellow line).

On Dec. 6, the volatile smile looked more like a smirk, with greater implied volatility on options at lower strikes, a sign of stronger demand for downside protection.

The smirk had since vanished due to a decline in demand for puts and an increase in demand for calls.

"Last week, we reported that the move towards a more neutral volatility smile for BTC was due to a drop in the IV of OTM puts rather than an increase in the IV of OTM calls. At the same time, we noted that a fall in implied vol across all strikes saw the implied volatility of the entire smile drop," Melville noted.

"Since then, we have seen a rise in the IV of OTM calls to the same levels they recorded at the beginning of December. However, OTM puts have remained at their lower levels, resulting in a reduction in the smile's skew," Melville added.

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