Funding Timing and No-Arbitrage Bounds in DeFi Perpetuals

This repository contains the paper and replication code for Funding Timing and No-Arbitrage Bounds in Decentralized Perpetual Markets.

The paper studies when no-arbitrage restrictions for decentralized perpetual futures have empirical content. The central mechanism is the timing of funding determination: Drift is the observable-funding case, where the next funding transfer is known at entry, while dYdX v4 is the forward-looking-funding case, where only an entry-time guaranteed cap or floor can enter the arbitrage bound.

Repository Layout

defi-perps/
├── paper/
│   ├── main.tex                  # source of truth for the paper
│   └── figures/                  # figures included by main.tex
├── drift/
│   ├── collection/               # Drift public archive fetchers
│   └── analysis/                 # Drift notebooks, robustness scripts, outputs
├── dydx/
│   ├── collection/               # dYdX public indexer fetchers
│   └── analysis/                 # dYdX notebook, cap robustness script, outputs
├── analysis/
│   └── verify_intro_stats.py     # checks introduction volume statistics
├── notes/
│   └── table_figure_manifest.md  # source map for tables and figures
├── Makefile
├── requirements.txt
└── README.md

Raw data files, LaTeX build artifacts, virtual environments, and local machine files are intentionally not tracked.

Quick Start

Install Python dependencies:

python3.11 -m venv venv
source venv/bin/activate
pip install -r requirements.txt

Compile the paper from the project root:

make paper

This runs latexmk inside paper/ and builds paper/main.pdf.

Data Sources

Drift Protocol

The Drift analysis uses public Drift S3 archive records.

• Markets: BTC-PERP, ETH-PERP, SOL-PERP
• Sample window: 2023-01-01 through 2024-12-31
• Frequency: hourly funding records
• Main fields: markPriceTwap, oraclePriceTwap, fundingRate, fundingRateLong, fundingRateShort, and timestamp

Fetch Drift funding records:

python drift/collection/fetch_funding_records.py

Fetch Drift trade records used for cumulative volume checks:

python drift/collection/fetch_trade_volumes.py

dYdX v4

The dYdX analysis uses the public dYdX v4 indexer.

• Markets: BTC-USD, ETH-USD, SOL-USD
• Sample window: 2023-10-26 UTC through 2025-12-30
• Frequency: hourly funding updates
• Funding endpoint: /v4/historicalFunding/{ticker}
• Candle endpoint: /v4/candles/perpetualMarkets/{ticker}
• Market-parameter endpoint: /v4/perpetualMarkets

Fetch dYdX funding, candle, and market-parameter data:

python dydx/collection/dydx_fetch_funding_records.py --out-dir ./data/raw/dydx

Raw data are not redistributed with the repository because they are large and reconstructible from public protocol or indexer sources.

Empirical Design

The deterministic theorem is implemented statistically using high-probability empirical bands. The residual basis parameter \hat{\Gamma} is calibrated as a 99th percentile on a training window and then held fixed for out-of-sample evaluation.

Protocol	Training window	Test window	Main empirical object
Drift	2023	2024	Out-of-band exits from high-probability empirical bands
dYdX	2023-10-26 to 2024-12-31	2025	Clamped-regime coverage and cap proximity

For Drift, the empirical ratio is markPriceTwap / oraclePriceTwap. The implementation sets the oracle TWAP ratio rho_k to 1 because the public Drift archive used here does not expose a synchronous instantaneous oracle price for each funding record.

For dYdX, the analysis treats historicalFunding records as hourly funding updates. The protocol cap is specified as an 8-hour-normalized quantity, with hourly cap eta_1h = eta_8h / 8.

Reproducing Tables and Figures

Rebuild the Drift analysis:

jupyter nbconvert --execute drift/analysis/test1_bounds.ipynb --to notebook --inplace
python drift/analysis/robustness_checks.py

Rebuild the dYdX analysis:

jupyter nbconvert --execute dydx/analysis/dydx_test1_bounds.ipynb --to notebook --inplace
python dydx/analysis/cap_robustness.py

The table and figure source map is in notes/table_figure_manifest.md. It lists the script, input data, sample window, and output file for each empirical table and figure in the paper.

Some small generated CSV tables are tracked because they are directly used for appendix robustness checks. Large raw datasets are ignored and should be regenerated from the public sources above.

Headline Replication Targets

The main Drift test window contains 8,774 BTC observations, 8,773 ETH observations, and 8,773 SOL observations. With the baseline 99th percentile \hat{\Gamma} calibration, the out-of-band rates are:

Market	Out-of-band rate
BTC-PERP	4.55%
ETH-PERP	3.21%
SOL-PERP	5.02%

The dYdX sample contains 57,330 hourly funding records across the three markets. In the 2025 test window, the funding cap never binds. Maximum absolute hourly funding reaches 8.96% of cap for BTC-USD, 3.62% for ETH-USD, and 2.27% for SOL-USD. The cap-tightening robustness script shows that even a tenfold tightening leaves zero clamped observations in the test window.

Source of Truth

The current paper source is paper/main.tex. Generated LaTeX files, including paper/main.pdf, are build artifacts and are not tracked.

Use:

make paper

to rebuild the PDF after editing the paper.

Citation

If you use this repository, please cite the working paper:

Erez, E. and Smirnov, M. Funding Timing and No-Arbitrage Bounds in
Decentralized Perpetual Markets.