MAT 292 Project: Bitcoin Spread Analysis: Delay Differential Equation Framework

Authors: Nicholas Nguyen [1010900474], Jay Patel [1010960872], Nelson Siu [1010940608]

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Table of Contents

• Overview
• Project Structure
• Data Description
• Installation
• Usage
• Output Files
• Dependencies

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Overview

MAT292 Project analyzing Bitcoin price spreads between Bitfinex and Gemini exchanges using a Delay Differential Equation (DDE) framework.

Project Structure

MAT292-Project/
│
├── data/                                    # Data files
│   ├── Bitfinex Week - minute ticker - Sheet1.csv   # Raw Bitfinex data (minute resolution)
│   ├── Gemini Week - minute ticker - Sheet1.csv     # Raw Gemini data (minute resolution)
│   ├── interpolated_second_data.csv         # Interpolated second-resolution data
│   ├── synchronized_spread_data.csv         # Synchronized spread time series
│   └── calibration_results.csv              # Parameter estimates from calibration
│
├── figures/                                 # Generated plots
│   ├── mid_prices.png                       # Price series from both exchanges
│   ├── spread.png                           # Spread time series
│   └── fig_k_and_tau.png                    # k estimates vs lag with critical delays
│
├── Python Scripts                           # Analysis pipeline
│   ├── process_spread.py                    # [1] Synchronize data and compute spread
│   ├── interpolate.py                       # [2] Interpolate minute data to seconds
│   ├── calibrate_k_tau.py                   # [3] Estimate k, τ, and compute τ_c
│   ├── plot_price_series.py                 # Visualize exchange price series
│   ├── plot_spread.py                       # Visualize spread dynamics
│   └── plot_k_tau.py                        # Plot k and critical delay estimates
│
├── LaTeX Files                              # Report generation
│   ├── matproject.tex                       # Main LaTeX document
│   └── *.aux, *.fdb_latexmk, *.fls          # LaTeX auxiliary files
│
├── requirements.txt                         # Python dependencies
├── context.md                               # Project context and rubric
└── README.md                                # This file

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Data Description

Source Data:

• Bitcoin (BTC-USD) price data from Bitfinex and Gemini exchanges
• Time period: March 9–17, 2022 (one week)
• Original resolution: 1 minute (OHLC data)
• Processed resolution: 1 second (via linear interpolation)

Installation

Prerequisites

• Python 3.7 or higher
• pip package manager

Setup

1. Clone or download this repository

2. Create a virtual environment (recommended):

   python -m venv .venv

3. Activate the virtual environment:

   • Windows (PowerShell):

     .venv\Scripts\Activate.ps1

   • Windows (Command Prompt):

     .venv\Scripts\activate.bat

   • macOS/Linux:

     source .venv/bin/activate

4. Install dependencies:

   pip install -r requirements.txt

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Usage

Complete Analysis Pipeline

Run the scripts in the following order to reproduce all results:

Step 1: Process and Synchronize Spread Data

python process_spread.py

• Loads raw Bitfinex and Gemini data
• Computes mid-prices
• Synchronizes timestamps
• Calculates spread (mA - mB)
• Output: data/synchronized_spread_data.csv

Step 2: Interpolate to Second Resolution

python interpolate.py

• Performs linear interpolation from minute to second resolution
• Generates high-frequency approximation
• Output: data/interpolated_second_data.csv

Step 3: Calibrate DDE Parameters

python calibrate_k_tau.py

• Estimates empirical delay (τ_emp) via cross-correlation
• Estimates mean-reversion rate (k̂) using multiple methods
• Computes critical delay (τ_c = π/(2k̂))
• Performs sensitivity analysis across different lag assumptions
• Output: data/calibration_results.csv, console summary

Step 4: Generate Visualizations

python plot_price_series.py   # Price series from both exchanges
python plot_spread.py          # Spread dynamics over time
python plot_k_tau.py           # Parameter estimates vs lag

• Outputs: Figures saved to figures/ directory

Visualization Scripts (Individual)

# Plot mid-prices from both exchanges
python plot_price_series.py

# Plot the spread time series
python plot_spread.py

# Plot k estimates and critical delays
python plot_k_tau.py

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Output Files

Data Files:

• data/synchronized_spread_data.csv - Aligned mid-prices and spread from both exchanges
• data/interpolated_second_data.csv - Second-resolution interpolated data
• data/calibration_results.csv - Estimated parameters (k, τ_emp, τ_c)

Figures:

• figures/mid_prices.png - Bitfinex and Gemini price series
• figures/spread.png - Spread time series visualization
• figures/fig_k_and_tau.png - Parameter sensitivity analysis

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Dependencies

All dependencies are listed in requirements.txt:

requests
pandas
matplotlib
numpy
scipy