Ten catalogued derivatives, each modified to death — and a single law for where the money actually goes.
Finance earns a fee on every component bolted onto a bespoke instrument. The industry calls these components innovation. The research question of the Blaque Baux Block program is narrower and more useful: for each modification, does the added component pay the buyer, or the desk?
We took the catalog's signature structures and varied each one on real data or a market-standard model — long against short, hedged against naked, plain against exotic — and scored every version with the same fat-tail toolkit (P&L, skew, drawdown, crisis-correlation, and Jensen's alpha). Across all ten variations, one finding held without exception. A modification never conjures return. It relocates risk onto an axis the buyer isn't watching — and the fee is the price of that relocation, collected wherever the brochure isn't pointing.
The law. A derivative modification does not create value; it moves risk to one of three places — the tail, an unobservable mark, or the funding leg. The discount, the enhancement, the "cost saving" is that risk, priced out and carried somewhere the buyer discounts.
Every structure in the study resolves onto one of four outcomes. Three are places to hide risk; the fourth is the honest case, where a modification genuinely serves the buyer and is fairly priced.
Reshaped, hidden below the sample, or re-sold. Looks calm; detonates in the crash.
Value lives in a parameter the buyer can't observe — a volatility or correlation input.
No option in sight — the risk is in the financing leg or a persistent basis.
The modification actually reduces risk, or is uncorrelated by construction. Fairly priced.
Straddle variants tail
No edge at fair pricing — every variant is ±0.2 Sharpe noise; the entire return is implied>realized. The short strangle "wins" +0.92 Sharpe in-sample — and that is the trap: its catastrophe simply isn't in the monthly bars, but SVXY lived it (−95%, 2018).
The underlying finishes between the two breakevens. The short seller keeps the premium.
A large move breaches a wing. Losses grow as the market moves farther from strike.
Delta-hedged short straddle tail
The one modification that genuinely improves — stripping directional noise lifts the Sharpe on the same premium (+0.21 → +0.48). But it cleans the harvest, it doesn't make selling vol safe: the short-gamma tail is untouched.
Delta hedging removes directional drift, leaving a cleaner volatility premium harvest.
Rebalancing cannot remove the short-gamma loss when the underlying moves sharply.
Calendar & diagonal — daily marks tail
On daily marks the far wings pay exactly in the crisis — COVID's −21.6% naked drawdown becomes the diagonal's +6.9% gain. But full-sample the diagonal's carry grinds a −43% drawdown vs the naked −29%: a ruin-aversion trade, not a free cap.
The long-dated protection is unused while repeated short-dated carry erodes the position.
A crisis move activates the wing and caps the naked loss, as the COVID window demonstrated.
Variance vs vol swaps tail
"Fair" pricing is a loser (vol −0.66, var −0.92 Sharpe) — trailing realized under-forecasts the forward. And convexity is terminal: a spike costs the variance swap ~k² vs the vol swap's ~k (worst month −1779% vs −333%). The vol swap dominates.
The short position collects the spread when realized volatility stays below the swap strike.
The vol swap loss rises roughly linearly. The variance swap loss accelerates quadratically.
Moneyness is shown as an option-style analogue; volatility and variance swaps are forwards on realized measures.
Swaptions tail ×2
A real rate vol-premium (short straddle +0.17 → +0.89), but rates have two tails: the violent one is the receiver / rates-down side (worst −16%, the 2020 bond spike), the payer / rates-up side a slow grind (2022 −17%). Tested against its own worst year, in-sample.
The terminal swap rate stays near strike, so the short straddle keeps its premium.
Rates down activate the receiver tail. Rates up activate the payer tail.
CMS — the convexity fee mark · σ
The convexity adjustment is real (Jensen; a 10y CMS carries ~25bp). But the margin hides in the vol mark — the same 10y is 9bp at σ=15% and 49bp at σ=35%. The CMS spread option tells the same story on correlation (value swings 51% across ρ). The fee is a mark, not a charge.
A low assumed σ produces a small convexity adjustment and a lower quoted value.
A high assumed σ expands the adjustment. The economics move through an unobservable input.
A CMS itself has no formal ITM or OTM state. These panels show low-mark and high-mark valuation regimes.
CDS index tranches mark · ρ
Tranching creates nothing — Σ tranche loss = portfolio expected loss, exactly; it only redistributes. The senior "AAA safety" is a correlation bet: the super-senior loses 0.0% at ρ=0.1 → 1.8–3.9% at ρ=0.9. In 2008 ρ→1 and the impossible AAA losses simply happened.
Portfolio losses remain beneath the tranche attachment point, so the senior layer is untouched.
Correlated defaults push loss through attachment. The tranche absorbs loss until detachment.
CDS tranches use attachment and detachment points, not conventional option moneyness.
Crack · Asian · three-way collar honest tail
The full range in one block. The crack spread is honest exposure (equity-corr +0.05, positive skew). The Asian option pays the buyer — averaging cuts vol, so it's 44% cheaper and the discount is fair. The three-way collar is the trap: re-selling a deep put reopens the tail (worst −61% vs a plain collar's −10%).
The underlying stays above the deep put strike. The collar appears protected and inexpensive.
The market falls through the lower strike. Protection ends and downside reopens.
The chart isolates the three-way collar. The crack spread is linear exposure; the Asian option uses average price versus strike.
Target-forward & barrier put tail
The corporate-hedge killers. The TARF caps the gain at +5% and leverages the loss to −303% (skew −1.56). The down-and-out put is 23% cheaper because the discount is the coverage: in the windows that actually crashed, it paid 0.0% where a vanilla put paid 6.9%.
The FX rate stays above strike. The hedge is unused and the TARF gain is capped.
The rate falls, but crossing the barrier removes the discounted put exactly when protection matters.
TRS & cross-currency basis funding
No option tail — the risk is the financing. A total return swap costs ~0.4%/yr, but the margin tail wipes 3× leverage in COVID and 5× in 2020 and 2022 (Archegos). The cross-currency basis is a fee for balance-sheet scarcity that gaps to −140bp in stress — quiet premium, then a gap. (Not ETF-observable; stated, not faked.)
Asset return exceeds financing and margin remains manageable. The position behaves nearly linearly.
Asset loss triggers margin while the cross-currency basis gaps. Leverage forces nonlinear liquidation.
TRS and cross-currency basis positions are linear or funding-dependent, so ITM and OTM are scenario analogues only.
| # | Structure | Block | Where the fee lives | The tell |
|---|---|---|---|---|
| 01 | Straddle variants | Vol | tail | strangle +0.92 in-sample; SVXY −95% |
| 02 | Delta-hedged short | Vol | tail | +0.21 → +0.48 Sharpe (cleaner, not safe) |
| 03 | Calendar / diagonal | Vol | tail | COVID −21.6% → +6.9%; full −43% |
| 04 | Variance / vol swap | Vol | tail | var worst −1779% vs vol −333% |
| 05 | Swaptions | Rates | tail ×2 | receiver −16% / payer grind −17% |
| 06 | CDS index tranche | Credit | mark · ρ | super-senior 0.0% → 3.9% on ρ |
| 07 | CMS | Rates | mark · σ | 10y CMS 9bp → 49bp on σ |
| 08 | Crack / Asian / 3-way | Cmdty | honest · tail | Asian −44% fair; 3-way −61% |
| 09 | TARF / barrier put | FX | tail | TARF +5% cap / −303%; DO put 0.0% |
| 10 | TRS / xccy basis | Linear | funding | 5× wiped 2020+2022; basis −140bp |
Four structures broke the pattern — and each broke it for the same reason. The Asian (average-rate) option and the average-rate forward genuinely reduce risk: averaging cuts the effective volatility (≈ /√3), so the lower price is fair. The crack spread is honest exposure — near-zero equity correlation and positive skew. The weather derivative has ~zero market beta by construction. Where a modification truly lowers risk, or is uncorrelated by design, it is priced fairly and pays the buyer. Everywhere else, the "saving" is the risk, relocated.