Event-Time Accounting for Two-Leg Perpetual Positions: Quantity Closure, Asynchronous Settlement and Evidence Levels

Hang Liu

doi:10.5281/zenodo.23932841

Abstract161 words

A two-leg result is meaningful only after quantity, clocks, currency, and evidence agree.

Two-leg perpetual positions are often evaluated by matching quote-currency notionals and extrapolating a displayed funding-rate spread. That practice can leave residual quantity, omit eligible funding events, double-count execution costs, and turn unavailable evidence into zero. This methods note develops an event-time ledger for linear, same-settlement-currency perpetual pairs. It combines common-base-quantity closure, four depth-walked fills, per-event funding eligibility, a closed-position identity, a basis-minus-crossing decomposition, scenario-consistent error attribution, and explicit evidence labels. Deterministic examples show that symmetric enumeration produces 7.20 USDT rather than 0.20 USDT in an eight-hour toy window and that a direction-fixed “oracle” need not be an upper bound. A bounded illustration using three routes and two mutually exclusive arms on one day yields net-before-funding paper results from −24.93 to −89.91 USDT. These are not independent trades or portfolio returns. Official settlement marks, account fee evidence, and real orders are absent; exact account net remains unavailable. The framework separates accounting validity from statistical or economic validation.

阅读中文摘要

双腿永续头寸常以报价币种名义金额配对，并外推当前资金费率差，但这种做法可能留下未平仓数量、漏算符合条件的资金费事件、重复扣减执行成本，并把缺失证据误写为零。本文提出适用于线性、同一结算币种永续合约组合的事件时间账本：以共同基础资产数量完成闭合，使用四次逐档盘口成交，逐事件确认资金费资格，并建立闭合头寸恒等式、基差减跨越成本分解、情景与结果误差归因及证据等级。确定性示例显示，在八小时玩具窗口内，对称事件枚举得到 7.20 USDT，而只计首次收入得到 0.20 USDT；固定原方向的“完美预测”也不构成真正的方向自由选择上限。一个仅含三条路线、两个互斥持仓臂和单个交易日的公开盘口纸面示例，其计费前净额介于 −24.93 至 −89.91 USDT；这些记录不是独立交易或组合收益。由于缺少官方结算标记价、账户费率证明和真实订单，精确账户净额保持不可用（NA）。本文区分会计恒等式成立与统计、经济有效性成立，不构成投资建议。

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Paper contents

I · Research question

A quote-currency match is not necessarily a closed position.

A long perpetual on one venue and a short perpetual on another can reference the same asset while using different multipliers, lot steps, funding schedules, valuation marks, and fee bases. Spending the same number of USDT at exit does not guarantee buying or selling the entry quantity. The residual exposure is not slippage; it is a different position.

The research question is therefore elementary but decisive: what accounting contract must hold before funding, execution, and price components can be summed without changing the position, event window, or evidence state? The answer is a common-base-quantity, event-attributed, scenario-keyed ledger—not a more sophisticated display of the latest rate spread.

Research 01 asks how executable net carry is measured. Research 02 asks how net-carry cases are framed. This paper asks whether the underlying ledger is closed and attributable in the first place.
Read Research 02: Framing Net Carry

II · Framework

One closed quantity. One event-attributed ledger.

The central identity is additive only after every component shares one scenario key. Price P&L is decomposed into basis change minus crossing; funding is added once per eligible event; four execution fees and other measured cash costs are deducted once. Crossing is already inside the four VWAPs and is not deducted again.

Closed-position identity

Π = B − X + C − Φ − O

Quantity closure

Both legs use one feasible base quantity Q. Entry and exit each walk two books at that same Q; insufficient depth produces an incomplete fill, never a fabricated last-level execution.

Four fills

Event-attributed funding

Expected event time, venue-recorded settlement time, and local receipt time remain distinct. Receipts and payments are enumerated symmetrically, with one-to-one record matching.

Cash timing

III

Scenario error attribution

A current-state scenario uses only information known at its timestamp. The later gap separates funding, basis, crossing, fee, and other-cost changes rather than becoming one undifferentiated “slippage” number.

Same key

Evidence and joint-risk semantics

Official cash, snapshot proxies, four-book paper values, and actual fills are not interchangeable. Covariance is not assumed to be zero, and a signed accounting vector is not a calibrated probability distribution.

Evidence first

NA is not zero, and a proxy is not official cash.

A verified empty funding event set supports zero. A missing settlement mark supports NA. A stablecoin-parity scenario is not realised USD profit, and an unchanged-current-state scenario is not a future fill.

III · Figures

Accounting controls, numerical illustrations, and their limits.

01 / 06

Two-leg event-time ledger with four common-quantity fills and matched funding events — Figure 1
Four fills close one common base quantity, while eligible funding events are matched one-to-one. Schematic only; no market observations.

Full event enumeration gives 7.20 USDT while first-receipt truncation gives 0.20 USDT — Figure 2
Eight hourly receipts and one eight-hour payment produce 7.20 USDT in full enumeration and 0.20 USDT under truncation. Deterministic example.

Six route-arm net-before-funding paper results ranging from minus 24.93 to minus 89.91 USDT — Figure 3
All six route-arm accountings were negative before funding. These are correlated counterfactuals, not independent trades or a portfolio. Source: 15 October 2026 public-book summary.

Route A execution overestimate decomposed into basis, crossing, and fee components — Figure 4
Route A's baseline overestimate is 11.25 USDT. Displayed components sum to 11.244; the 0.006 display-rounding difference is retained.

Official cash, snapshot proxy, four-book paper, and actual fills have different evidence meanings — Figure 5
Evidence labels are not a universal ranking. NA means unavailable; a verified empty event set means measured zero; a missing record does not mean no event.

Surrogate selects candidate B while the final objective selects candidate A — Figure 6
A surrogate selects B, while the final objective including basis selects A. Deterministic counterexample; not an observed trade.

Scroll horizontally or use the arrows. Select a figure to inspect its details.

IV · Evidence boundary

Accounting validity is not out-of-sample performance.

The paper validates identities and rejection rules. It does not validate a return estimator, a forecasting model, or a live execution strategy. Three routes and two arms on one day cannot identify a win rate, an opportunity frequency, a portfolio Sharpe ratio, or a stable market effect.

Established by deterministic calculation

Quantity closure, four-fill VWAP accounting, symmetric funding, B−X, scenario error budgets, NA propagation, covariance-sensitive variance, and final-objective consistency.

Bounded public-book illustration

Six route-arm net-before-funding values range from −24.93 to −89.91 USDT. RSR funding is a frozen-mark proxy; BTC's zero is a verified empty event set. Exact account net is NA throughout.

Not claimed

No live fills, account fees, official settlement marks for RSR, independent pre-result timestamp, multi-day robustness, third-venue comparison, predictive out-of-sample result, confidence interval, or multiple-testing result.

Signed scenario error

D_exec = −ΔB + ΔX + ΔΦ

Positive values mean that the unchanged-current-state scenario was too favorable; negative values mean that the subsequent paper result was better.

V · Limitations

A reproducible accounting contract—not a live-system specification.

Instrument scope. Inverse, quanto, continuously accruing, specially adjusted, liquidated, and unresolved mixed-currency positions require separate adapters or NA/UNSUPPORTED.
Execution scope. Public books do not model queue position, reaction, hidden liquidity, partial fills, financing, transfers, liquidation, or capital limits.
Protocol scope. The local hash preceded entry, but the external receipt arrived after the version-2 freeze and short-arm result. Independent pre-result timestamping remains outstanding.
Reproduction scope. The package recomputes summary tables and deterministic tests. Raw archived books were not supplied, so raw-book replay is not claimed.
Statistical scope. No predictive estimator or candidate model set is defined; out-of-sample tests, multiple-testing controls, and dependence-aware inference remain future work.

This paper is for research and methodological information only. It does not provide investment, legal, accounting, or tax advice; does not recommend any trade, venue, leverage, or position size; and does not promise income, execution, capital protection, or protection from liquidation.

Event-Time Accounting for Two-Leg Perpetual Positions