Stochastic Thermodynamics of Price Impact

This repository contains the numerical implementation and validation code for the paper "A Stochastic Thermodynamics Approach to Price Impact and Round-Trip Arbitrage: Theory and Empirical Implications.https://arxiv.org/abs/2512.03123"

The code verifies the Financial Second Law and the Fluctuation Theorems derived in the paper by simulating trading trajectories under linear permanent impact and strictly convex temporary impact.

Repository Contents

quant.py: A Python prototype for rapid verification and plotting.
quant.cpp: A high-performance C++ implementation for production-grade simulation.

Key Features

Work Calculation ($W$): Computes dissipated work ($\eta \int v_t^2 dt$) numerically.
Variance Calculation ($V$): Computes position variance ($\int q_t^2 dt$) via Riemann sums.
Fluctuation Bound: Calculates the exponential bound $P(\Pi \ge 0) \le \exp(-W^2 / 2\sigma^2 V)$.
Strategies Verified:
- Triangular Strategy: (Buy-then-sell linear/symmetric).
- Ramp Strategy: (Smooth linear decay trading rate).

Prerequisites

Python

Python 3.x
NumPy (pip install numpy)

C++

GCC (g++) or any standard C++11 compliant compiler.

How to Run

1. Python Simulation

Run the script to see the comparison between Numerical integration and Analytical formulas.

Expected Output

--- TRIANGULAR STRATEGY --- Work (Numerical): 100.0000 Work (Analytical): 100.0000 Var (Numerical): 8333.3333 Var (Analytical): 8333.3333 Fluctuation Bound: 1.499622e-07 Accuracy check: PASS

--- RAMP STRATEGY --- Work (Numerical): 33.3333 Work (Analytical): 33.3333 Var (Numerical): 3333.3333 Var (Analytical): 3333.3333 Fluctuation Bound: 1.888756e-02 Accuracy check: PASS

C++ Simulation

Compile and run the high-performance implementation.

g++ -o quant quant.cpp ./quant

Theoretical Alignment

This code strictly adheres to the corrected Linear Permanent Impact assumption ($\mathcal{I}(v) = \lambda v$). Under this framework, the permanent impact component integrates to zero over any closed round-trip cycle, meaning the dissipated work is governed solely by the temporary impact coefficient $\alpha = \eta$.

License

MIT License.

Free to use for academic and research purposes.