Tail Body Ratio: A Different Signal At Every Tenor

A regime label is supposed to save you work. Read one field, see TAIL_EVENT, and you know somebody is paying up for crash protection. We counted how often that label actually fires across 726,016 ten-minute cycles on six coins, and it fires on 82.6% of two-month readings against 9.7% of front-week ones. Same field, same threshold, four different instruments.

This note takes Cayø Largo's own tail body ratio apart by expiry bucket. We report the firing rate of every label at every tenor, then show why a fixed threshold cannot divide a distribution whose median more than doubles across the curve. After that comes the two-stage rule the labels actually run on, and the availability problem sitting underneath all of it. Everything here is measured against our archive between 13 January and 11 September 2026.

The measure, and why the tenor matters

The tail body ratio divides deep put skew by 25-delta put skew. It is the field Cayø Largo uses to say whether tail risk in crypto options is being bought in one place or everywhere at once. Both of those inputs are excesses over at-the-money, so the field is a ratio of two differences, not a ratio of two prices.

$$R(\tau) = \frac{\sigma_{\text{FAR}}(\tau) - \sigma_{\text{ATM}}(\tau)} {\sigma_{25\Delta P}(\tau) - \sigma_{\text{ATM}}(\tau)}$$

where $\sigma_{\text{FAR}}$ is the implied volatility of the far below-the-money cohort, $\sigma_{25\Delta P}$ that of the 25-delta put, $\sigma_{\text{ATM}}$ the at-the-money level, and $\tau$ the time to expiry. Written that way, two things are already visible. The numerator is the price of the far wing of the volatility surface, the strikes a desk buys when it wants insurance against a move that has not happened in years. That far wing is thinly quoted and moves for reasons that are not always information, which is why we have argued separately that deep out-of-the-money implied volatility momentum is noise rather than signal. The denominator is the near wing, the ordinary 25-delta put that a book buys and sells every day. Dividing one by the other asks a clean question: is the downside money concentrated out in the tail, or spread across the body? The second visible thing is the denominator, and we come back to it at the end, because nothing in that expression stops it reaching zero.

That question only has meaning inside one expiry. This is not a subtlety we invented. Back in 2014 Gavin at Options Trading IQ defined the smile as the difference in implied volatility between strikes on the same security with the same expiration date. His worked example is a single month of SPY options, namely, one tenor and nothing else. Six years later Su Zhu made the same move on crypto. Writing on Deribit Insights, he defined the 25-delta measure as a comparison of a call and a put of the same expiry, and then plotted one-month, three-month and six-month skew as three separate lines. Have a look at that chart and the three sit at visibly different levels. Nobody in either archive averaged them together.

There is also a mechanism, and Su Zhu states it in the same piece. A deep out-of-the-money option has no intrinsic value at all, so its entire price is time value. Give the far wing more time and you give it more of the only thing it owns. The near wing gains too, but it starts from a base that is already partly anchored to spot. The ratio between them should therefore rise with tenor, and it does.

What the tail risk label says at each expiry

Here is the firing rate of each label, by expiry bucket, over the full archive.

Expiry bucket	TAIL_EVENT	BROAD_PANIC	INSTITUTIONAL_HEDGE	NORMAL	No reading	Cycles
7 days	9.7%	45.6%	25.4%	8.1%	11.2%	205,134
30 days	80.5%	2.0%	0.2%	5.7%	11.7%	201,435
60 days	82.6%	0.6%	0.0%	1.9%	14.8%	162,572
180+ days	77.2%	0.4%	0.0%	7.0%	15.4%	156,875

Figure 1: Each bar is one expiry bucket and each segment is one label's share of the cycles in it. The front week distributes across four states. Everything past a month is one gold block with rounding on the edges.

Read the bottom three rows and the label has stopped working. A state that describes four cycles in five is not a regime, it is the weather, and weather is not something a desk trades. Beyond one month the crypto options surface is permanently tail-bid, and saying so every ten minutes adds nothing a desk can act on.

The failure has a shape any observational astronomer would recognise. Leave the shutter open long enough and every object in the field clears your detection threshold, and the plate comes back saying everything is bright. The cutoff has not changed, the exposure has, and that is the whole difficulty with reading a fixed number against a book that has been given more time to move.

The front week is the interesting row, and it is interesting for the opposite reason. There the label spreads across four genuine states, with BROAD_PANIC the most common at 45.6%. One of those four barely exists anywhere else. INSTITUTIONAL_HEDGE covers 52,091 front-week cycles, one quarter of them, and then almost vanishes. Four observations at sixty days. Eleven past six months. In eight months of continuous sampling.

How the classifier really works, in two stages

The label is not one rule but two, and only the first is a threshold. Cayø Largo's API reference gives the first: a ratio above 3.0 marks concentrated far-wing buying. Run that rule across the archive and it does exactly what it claims. Written as an indicator, the rule and its firing rate are

$$\mathbb{1}\!\left[R(\tau) > 3\right], \qquad \Pr\!\left(R(\tau) > 3\right) = 1 - F_\tau(3)$$

where $F_\tau$ is the cumulative distribution of the ratio inside expiry bucket $\tau$, and $\mathbb{1}[\cdot]$ takes the value one when the condition holds and zero otherwise. That probability should equal the share of cycles the pipeline flags as something other than quiet, and it does, to within rounding.

Expiry bucket	Cycles with ratio above 3.0	Cycles labelled TAIL_EVENT or BROAD_PANIC
7 days	53.1%	55.3%
30 days	82.4%	82.4%
60 days	83.1%	83.2%
180+ days	77.2%	77.6%

Stage one decides whether anything fires at all. A second rule decides which of the two labels it gets. Take every reading above 3.0 and ask which one it received. At thirty days, 97.7% come back TAIL_EVENT; at sixty, 99.4%; past six months, 99.8%. At seven days the same filter returns 18.4% TAIL_EVENT and 81.6% BROAD_PANIC, across 108,842 cycles. The ratio alone cannot produce that. Something beyond it is separating concentrated buying from buying spread across the book, and it does almost all of that work inside the front week.

No single reading will show you this. You need the base rate of each label at each tenor before either label means anything. The rest of this note supplies them.

Figure 2: The horizontal axis is the tail body ratio on a log scale, the vertical axis the share of cycles at or below it. Coral is the front week, the grey band spans the three longer buckets. The gold dashed line is the documented 3.0 threshold, and the squares mark each median.

A threshold is only a divider if it sits somewhere near the middle of what it divides. At 3.0 the line catches 10.2% of front-week readings and between 2.2% and 8.7% of everything longer. Past a month it does not cut the distribution at all. It marks the floor of it, which is the arithmetic behind the 80.5% and 82.6% in the first table.

The typical range moves with tenor, so quote it with the tenor attached. The mean ratio runs 6.55 at seven days, 16.86 at thirty, 22.30 at sixty and 19.14 past six months, and the medians run 6.0, 13.5, 15.5 and 13.5. At one month, 94.5% of clean readings exceed 5. A desk carrying a single "normal band" in its head will call almost every long-dated cycle abnormal, and the endpoint documentation now states these four ranges rather than one.

The same applies to the two active labels. BROAD_PANIC is not a low-ratio condition. Read it as one and you will find nothing: across every coin and every bucket in eight months its lowest ratio is 2.50 and its highest 25.81. It is the second stage firing, not the first. It lives in the front week, where the second stage has something to decide.

The field is not broken. Inside one tenor it orders the book correctly. What it will not do is carry a number across tenors, which is exactly what a single published threshold invites you to try.

The reading you cannot take

There is one more measurement, and it lands on the tenor that matters most. Return to the denominator. As an option approaches expiry the smile compresses toward the at-the-money level, so the near wing's excess over it goes to zero and takes the ratio with it.

$$\sigma_{25\Delta P}(\tau) - \sigma_{\text{ATM}}(\tau) \;\xrightarrow{\;\tau \to 0\;}\; 0 \qquad \Longrightarrow \qquad R(\tau) \longrightarrow \pm\infty$$

where the limit is taken as time to expiry shrinks to nothing. This is not a modelling nicety. It is why the front-week ratio reaches 5,941.89 at its maximum, against 25.81 for anything the pipeline will call broad panic. It is also why a large share of front-week cycles produce no number at all. When the denominator is too close to zero to divide by, the pipeline returns a sentinel instead.

Figure 3: Each row is one coin. The coral mark is the share of front-week cycles that return a sentinel instead of a ratio, the blue mark the same share at one month. The gap is the cost of reading the front of the book.

Coin	Front-week cycles	Sentinel	Share	Same share at 30 days
TRX	34,082	21,227	62.3%	1.7%
BTC	34,277	15,466	45.1%	12.8%
ETH	34,269	8,940	26.1%	1.5%
XRP	34,224	7,253	21.2%	1.4%
AVAX	34,104	4,495	13.2%	0.1%
SOL	34,178	3,170	9.3%	0.8%
All six	205,134	60,551	29.5%	3.1%

Bitcoin's front-week tail body ratio cannot be computed on 45.1% of cycles, 15,466 out of 34,277. The equivalent figure one bucket out is 12.8%. Two costs follow. It thins the one tenor where the label discriminates. It also punishes anyone who pulls the column into a dataframe and takes a mean, what quietly poisons every statistic built on it. Keep in mind that the sentinel is a large negative number, so it will drag an average anywhere it likes. Filter it before you touch it.

How this was measured

Every figure comes from deribit_options_oria_cohort_iv_skew, served through the vol/skew endpoint, read at Cayø Largo's native ten-minute cadence across BTC, ETH, SOL, XRP, AVAX and TRX. The window runs 13 January to 11 September 2026 and holds 726,016 cycles across the four expiry buckets the table names. Label shares are counted over all rows including nulls, so the columns sum to 100%. Ratio statistics exclude the ±9999 sentinel and are reported separately in the availability section, which is the only honest way to carry both. The current cycle carries data_quality_tier of COMPLETE on all six coins, with total_option_count between 50 and 212 depending on coin and bucket. The surface itself is visible live on the skew surface page.

Two counts in this note describe different things and are worth separating. Every percentage in the label table is a share of cycles within one expiry bucket. The shares in the sentinel table are of front-week cycles per coin. They are never the same denominator.

What this does not say

We have not shown that the tail body ratio predicts anything. This note measures a classifier against its own history, not the returns of a trade taken on it, and those are different studies. The second one is on the list.

The stage-two rule is ours and we are not publishing its inputs. What this note establishes is what it does: it separates concentrated buying from broad buying above the gate, and it does that almost entirely in the front week. What drives the separation is a longer subject. INSTITUTIONAL_HEDGE deserves its own note, not a paragraph at the end of this one.

A gate is a design choice, and 3.0 remains the right gate. It answers the question it was built for: is anything happening in the wings at all. Ranking within the tenor is what you build on top of that gate. It became possible when the archive grew long enough to carry a base rate per bucket. It was not, when the field shipped. That is what an archive is for.

Watch the shape, not the level

Vitor Gaspar put the general version of this well in July 2026, writing about vega on commodity books. Desks bucket by maturity, he argues, because the term structure moves as a shape, never as a level. In other words, a single number across maturities lies. Wing pricing behaves the same way. Amberdata reached the same place from the data side in 2023, and before plotting the 25-delta wings against at-the-money volatility as one line they normalised the series to a constant thirty days. The normalisation is the point. Without it there is no single line to draw.

Read the tail body ratio as a rank, not a level. Take the rank inside the tenor you trade, over a window you can state.

$$q_\tau(R_t) = \frac{\bigl|\{\, R_s \in W_\tau \;:\; R_s < R_t \,\}\bigr|}{\bigl|W_\tau\bigr|}$$

where $W_\tau$ is the set of past readings drawn from the same expiry bucket, $R_t$ is today's ratio, and the vertical bars count the members of a set. One line of code, and the only form in which one tail body reading is comparable to another. Eight is a high number on a front week and an unremarkable one at a month, and no label on its own will tell you which of the two you are holding. The threshold belongs to the field. The percentile belongs to you.

References

Gavin, Options Trading IQ, 29 January 2014, "Implied Volatility Smile." Defines the volatility skew as the difference between strikes on the same underlying sharing one expiration date, and illustrates it with one month of SPY options.

Su Zhu, Deribit Insights, 18 May 2020, "Explaining Skew when Considering BTC at 36,000 USD." Argues that a deep out-of-the-money option's entire value is time value, and charts one-month, three-month and six-month 25-delta skew as three separate series of the same expiry.

Amberdata, Deribit Insights, 24 January 2023, "Bitcoin Options: Finding edge in four years of volatility regimes." Calls the at-the-money term structure the spine of the surface and the out-of-the-money options its wings, and in the Spot/Vol Dynamics section ratios the 25-delta wings against at-the-money volatility, normalised to a constant thirty days.

Vitor Gaspar, LinkedIn, 25 July 2026, "Vega. The exposure hiding in every long-dated hedge." Argues that a single vega number across maturities is misleading and that desks must bucket by maturity, because the term structure moves as a shape rather than a level.