Module 8: Crypto Options
Volatility Smile, Skew, and Term Structure
Chapter 9 of 14 · about 5 minutes
9.1 Different strikes, different volatility
Mint looked closely at an options chain and noticed something strange. The at-the-money BTC options showed implied volatility of 55%. But options far below and far above the current price showed higher IV, some above 65%.
"Bitcoin can only have one future volatility," said Mint. "How can different options imply different volatilities?"
"Because the simple pricing model assumes all moves are smooth and evenly distributed," said Hash. "Real markets aren't like that. Traders pay extra for options that protect against big jumps, and the differences in IV across strikes and expiries tell you what the market is worried about."
9.2 The volatility smile
If you plot implied volatility against strike price for a single expiry, you often get a curve that rises at both ends, like a smile.
| Strike (BTC at $100,000) | Implied volatility (illustrative) |
|---|---|
| $70,000 | 68% |
| $85,000 | 60% |
| $100,000 | 55% |
| $115,000 | 58% |
| $130,000 | 64% |
This volatility smile shows that options far from the current price are relatively more expensive than the simple model would suggest. The reason: crypto prices make large jumps more often than the model assumes. Options that pay off in those jumps deserve, and get, a higher price.
Chapter 9 · Smile, skew, and term structure
Implied volatility is plotted against strike price, forming a smile that dips to its lowest near the at-the-money strike and rises toward both wings. The curve is skewed so out-of-the-money puts carry higher implied volatility than equivalent calls.
9.3 Skew
The smile is rarely symmetrical. Skew describes whether downside options (puts) or upside options (calls) carry higher implied volatility.
| Skew | Meaning | When it tends to appear |
|---|---|---|
| Put skew | Downside puts have higher IV than equally distant upside calls | Fear, uncertainty, after crashes, when holders seek protection |
| Call skew | Upside calls have higher IV than equally distant downside puts | Euphoria, strong rallies, when traders chase upside |
| Flat | Similar IV on both sides | Balanced sentiment |
In stock markets, put skew is almost permanent: investors always pay up for crash protection. In crypto, skew swings between puts and calls more often, because crypto has violent rallies as well as violent crashes. During strong bull markets, crypto calls have at times traded at higher IV than puts.
9.4 Measuring skew: risk reversals
A common way to measure skew is the 25-delta risk reversal: the implied volatility of a call with a delta of 0.25, minus the implied volatility of a put with a delta of −0.25 (Chapter 7). These are out-of-the-money options roughly the same "distance" from the current price.
Risk reversal = IV of 25-delta call − IV of 25-delta put
| Situation | 25-delta call IV | 25-delta put IV | Risk reversal | Reading |
|---|---|---|---|---|
| Fearful market | 52% | 62% | −10 | Strong demand for downside protection |
| Balanced market | 56% | 57% | −1 | Roughly neutral |
| Euphoric market | 66% | 58% | +8 | Strong demand for upside exposure |
"So the risk reversal is like a sentiment gauge," said Mint.
"One of the best in crypto," said Hash. "It shows what people are actually paying for, not just what they say on social media."
9.5 Term structure
Term structure describes how implied volatility changes across expiries, for at-the-money options.
| Expiry | ATM implied volatility, normal market (illustrative) | ATM implied volatility, crisis (illustrative) |
|---|---|---|
| 1 week | 48% | 95% |
| 1 month | 52% | 80% |
| 3 months | 56% | 68% |
| 6 months | 58% | 62% |
Upward-sloping (contango). In calm markets, longer-dated options usually have higher IV, reflecting more uncertainty over longer periods.
Inverted (backwardation). In crises, short-dated IV spikes above long-dated IV, because the market expects violent moves right now but calmer conditions later.
An inverted term structure is a sign of acute stress. When it flips back to normal, the panic is often easing.
9.6 Event kinks
When a known event is coming, such as a major economic announcement or a network upgrade, the expiry just after the event often shows a bump in IV compared with neighbouring expiries. This event premium reflects expected volatility from the event. After the event, it disappears, which is the volatility crush from Chapter 6.
| Expiry | ATM IV |
|---|---|
| Friday before the event | 50% |
| Friday after the event | 62% |
| Two weeks after the event | 54% |
By comparing these, traders can estimate how big a move the market expects from the event itself.
9.7 Why this matters for your trades
Buying protection. If put skew is steep, downside puts are expensive. A collar, which sells an upside call to help pay for the put, may be more attractive (Chapter 11).
Buying upside. If call skew is steep, upside calls are expensive. Call spreads, which sell a higher call to offset cost, can help (Chapter 13).
Selling options. Steep skew means the options you sell on that side pay more premium, but they're expensive for a reason: the market sees more risk there.
Choosing expiries. In an inverted term structure, short-dated options are expensive and longer-dated options relatively cheap. In normal conditions, the reverse.
9.8 Try it yourself
On a BTC options chain for a monthly expiry, record the implied volatility of puts and calls at five strikes below and above the current price. Plot them to see the smile. Is it skewed toward puts or calls? Then find the 25-delta risk reversal for BTC on a data site, if available, and check how it has changed over the past three months.
Finally, record ATM IV for four different expiries and describe the term structure.
Key takeaways from this chapter
- Implied volatility differs across strikes, often forming a smile, because crypto jumps more than simple models assume.
- Skew shows whether puts or calls carry higher IV; it reflects demand for downside protection or upside exposure.
- Crypto skew swings between puts and calls more than in stock markets.
- The 25-delta risk reversal is a useful gauge of options market sentiment.
- Term structure shows IV across expiries; normal markets slope upward, crises invert it.
- Known events create IV bumps in the expiries just after them.
- Skew and term structure affect which strategies, strikes, and expiries offer better value.