BL-SD-047: Harvesting the Volatility Premium

Status: RELEASED

Classification: PUBLIC

Revision: 1

Date: 2026-09-08

Venue: Bybit perpetuals, delta-hedge leg; Deribit options, premium leg Programme: II Verdict: CLOSED Axis of death: Capital Transferability: ENVELOPE-BOUND

1. Identification

D5a and H-V1 name the same measurement. The dossier keeps both codes for the reason the template requires: the internal code is the name research carried at the time, and this one was pre-registered and closed the same day the underlying economics were already known well enough to decide it.

2. Economic thesis

Selling volatility, structurally, means selling insurance against large price moves and collecting a premium for it. The premium exists because implied volatility, the market's price for that insurance, runs on average above the volatility that is subsequently realised. A seller who is not predicting direction, only underwriting the spread between implied and realised, should be compensated for bearing the risk that the two occasionally diverge sharply against the position.

Who is forced to lose, if the mechanism works as stated. Nobody is forced in the way a liquidated position or an adverse-selected maker is forced. The counterparty is a buyer of insurance who pays the premium voluntarily, in exchange for protection they value more than its price. This is a risk premium, not an informational edge, and the dossier does not claim otherwise.

3. Falsifiable claim

Pre-registered, in the same session that produced the closing figures:

The volatility risk premium on BTC is real, exceeds the round-trip cost of capturing it, and survives an exact-payoff simulation using actual price paths rather than an averaged approximation. If it does, the question that decides whether it is tradeable at this operator's scale is capital, not mechanism.

4. Mathematical specification

Notation per BL-D-011.
 
Realised variance risk premium, day t:
 
  VRP_t = IV_t(30d) - RV_{t, t+30d}          vol points, IV from Deribit DVOL,
                                              RV realised forward from the lake
 
Position: short ATM straddle, tenor T = 30 days, entry at t0, expiry t0 + T.
 
Unhedged payoff at expiry, path-independent:
 
  PnL_unhedged = premium(t0) - | S_{t0+T} - K |
 
Delta-hedged variant, daily rebalance at close, offsets d in {0, 10, 20} days
tested against fixed rebalance dates:
 
  PnL_hedged = PnL_unhedged
             + sum over rebalance days j of  [ -Delta_j * ( S_{j+1} - S_j ) ]
             - hedge_cost
 
  Delta_j    Black-Scholes delta of the straddle at day j, from mark IV at j
  hedge_cost perp fee (5.5 bps per side) times notional traded at each rebalance
 
Sizing:  one straddle per non-overlapping 30-day window, minimum 0.1 BTC contract
Cost:    entry_cost = 2.5 pct of premium (measured bid-ask plus fee, section 5)
         c_rt = entry_cost, applied once per position, not per rebalance

Causality holds for the signal itself: VRP_t uses only IV_t, observable at t, against a realised volatility that resolves forward and is used only to characterise the historical premium, not as an input to any live decision. The hedge variant is causal by construction, since each Delta_j uses only information available at day j.

One term is stated as a departure rather than reconstructed. The original cost-floor pass approximated the payoff as 0.4 * VRP * sqrt(T), which is a valid approximation for a delta-hedged position and an invalid one for an unhedged position held to expiry, whose payoff is a function of the terminal price alone and has no path term at all. The correction is recorded in section 13 because the direction of the error, and who caught it, is itself part of the record.

5. Operating envelope

Minimum contract size on BTC is 0.1 contracts, or 6,345 USD notional at the measured spot. That single figure, not a modelled one, is the number section 10 turns on.

6. Instrument

The variance risk premium characterisation and the cost-floor pass use the programme's option-pricing module, the option-pricing module, against Deribit's DVOL index and the research-era realised-volatility series already built for other rows. The exact-payoff simulation, the exact-payoff simulation, replays actual BTC price paths from six years of hourly klines through the straddle payoff directly, rather than through the averaged VRP approximation, specifically to capture the terminal-price dependence the approximation cannot.

7. Results

Variance risk premium, research era:

Exact-payoff simulation, 30-day ATM BTC straddles, offset 0, n=42, entirely in-sample:

Subperiod decomposition, hedged variant, three equal blocks: +22.6 pct, +20.9 pct, +20.1 pct. Materially more consistent across regime than the unhedged variant's +1.8 pct, -9.0 pct, +23.8 pct.

Pessimistic combination, three-day rebalance, 2 vol-point IV haircut, 5 pct entry cost:

The sign does not reverse under pessimistic assumptions. The edge is not strong enough, under those assumptions, to stand on its own.

8. Verdict, axis of death, and transferability

Verdict: CLOSED. Axis: capital. Transferability: ENVELOPE-BOUND.

Applying the BL-D-002 section 4 test: at this operator's declared capital scale, is the result positive? Yes, and by a wide margin on the delta-hedged variant, t=2.43 on 42 in-sample positions with a subperiod pattern that holds together across three separate stretches of the sample. Would a different capital scale change the answer? Also yes, and decisively: a single BTC contract at minimum size carries 6,345 USD of margin under an unbounded loss profile, against a declared working capital of 1,000 to 2,000. There is no room in this envelope to hold even one position, let alone the several non-overlapping positions the simulation itself requires to diversify away the tail risk the mechanism is priced to insure against.

This is the clearest capital-axis closure in the record. The mechanism is not in question; a t-statistic of 22 on the underlying premium is not a marginal finding, and few results in this archive were verified independently by as much of the existing literature. The operator was the wrong size for it.

9. Cost and capacity analysis

Entry cost, measured                2.5 pct of premium
Entry cost, earlier estimate        5.7 pct of premium, wrong tenor, superseded
Edge disappears near                10 pct of premium (research-era decomposition)
Margin required per BTC contract    6,345 USD, minimum size
Declared working capital            1,000 to 2,000 USD
Managed deployment estimate         50,000 to 100,000 USD

Capacity in the conventional sense, how much notional the market can absorb, was not the binding constraint and was not measured. The binding constraint is capital sufficient to hold the position at all, which this envelope does not supply.

A second, structural cost belongs here rather than in section 4, because it is a property of the tail rather than of the fee schedule: the worst positions in the simulated sample cluster on the same calendar dates for both BTC and ETH, consistent with a period of simultaneous cross-asset stress. Correlation of losses runs highest exactly when diversification across positions would matter most, which is a property of underwriting insurance generally and not a defect of this specific measurement.

10. Envelope sensitivity and reopening conditions

Binding parameter: capital scale, specifically margin per contract against declared working capital.

Reversal condition:  working_capital  >=  N * margin_per_contract
 
  margin_per_contract = 6,345 USD, minimum BTC size
  N                    number of non-overlapping positions needed to diversify
                        tail risk, not separately measured here but bounded
                        below by more than one

At the declared 1,000 to 2,000 USD, N is zero: the operator cannot open even a single position. The recommendation carried in the source material, and repeated here without alteration, is that a managed deployment of this mechanism needs 50,000 to 100,000 USD to hold multiple non-overlapping positions with any tail protection. That is roughly 25 to 50 times the programme's declared scale.

What would reopen it: working capital at or above that range, combined with the operational capacity to run daily delta-hedging discipline, since section 7's sensitivity table shows the edge is not robust to hedging less often than daily. A reader with that capital and that operational capacity inherits a mechanism this dossier has already verified twice, in an approximation and in an exact-payoff simulation.

What would not reopen it: a smaller minimum contract size alone. Even at a hypothetical smaller minimum, the unbounded loss profile of a short straddle means a single position is still a concentrated tail bet, and the consistency shown in section 7 depends on holding several non-overlapping positions, not one.

11. Reference implementation

The options cost-floor screen and the exact-payoff simulation are published as 05_INSTRUMENTS/strategies/python/src/volatility_premium.py, with 19 tests, on the option-pricing module 05_INSTRUMENTS/strategies/python/src/option_pricing.py, with 10. The rewrite corrects the payoff approximation documented in section 4 and section 13, and only the exact payoff is published. The approximation is described in the module's own change record, with what it did to the numbers, rather than shipped as live code a reader might reach for by mistake.

12. Evidence register

Evidence E-0009 referenced elsewhere in the archive against this row carries an identical simulation output and is not cited separately here.

13. Lessons extracted

The correction in section 4 is the lesson, and it corrects the record's own earlier diagnosis of itself. The cost-floor pass had described its own 0.4 * VRP * sqrt(T) approximation as optimistic because it ignores gamma and path-dependency. That diagnosis was imprecise. An unhedged short straddle held to expiry has no path-dependency at all; its payoff is a function of the terminal price alone. What the averaged model actually hides is starker: a single large terminal move erases dozens of small wins, and an averaged VRP figure cannot show that by construction. The unhedged simulation's maximum drawdown of -42.9 to -79.8 percent, against a modelled expectation of -5.3 percent, is the size of that miss.

The second lesson is procedural rather than statistical. This row was closed on a declared, already-known capital parameter rather than on a fresh statistical test, and it was closed the same day it was pre-registered. That is efficient rather than irregular: the capital constraint in BL-FM-002 section 6 was fixed before the programme began, and once the mechanism itself was confirmed at t=22 and t=2.43, no further measurement was needed to know that 6,345 USD of margin does not fit inside 1,000 to 2,000 USD of capital.

14. Cross-references

BL-P2-001 section 6, the door 5a narrative. BL-FM-002 section 6, the capital-scale declaration this verdict turns on. BL-SD-048 for door 5b, the conditioned variant of this same premium. BL-D-002 section 4 for the envelope-substitution test applied in section 8. Ledger rows D5a and H-V1.

Copyright (c) 2026 Bijective Labs. All rights reserved.