Market Making and Transient Impact in Spot FX

Battle Count: 82

Highly relevant to quantitative trading, particularly for FX market-making desks and algorithmic execution. The paper directly addresses the practical question of how dealers should optimally quote and hedge when market impact is transient rather than permanent. The finding that the pure internalization zone depends on the impact state has direct implications for real-time trading algorithms. The comparison between Almgren-Chriss and transient impact models provides actionable guidance for parameterizing execution algorithms. The work bridges theoretical stochastic control with practical FX desk operations.

The analytical framework (HJB equation, Riccati ODE, quadratic ansatz) is mathematically sophisticated but well-established in the literature. The numerical solution via explicit Euler in JAX is computationally efficient (sub-second). However, implementing the full system requires: (1) solving the coupled Riccati ODEs for A(t), B(t), C(t); (2) handling the multi-dimensional state space (inventory q, impact state x); (3) implementing the sigmoid intensity functions and their derivatives; (4) Monte Carlo validation with SDE simulation. The main complexity lies in correctly coupling the OTC quoting logic with the interbank hedging execution and the transient impact state dynamics.

The paper provides detailed parameter values (size ladder, intensity functions, volatility, risk aversion, execution cost parameters, impact decay rate) and describes the numerical method (explicit Euler in JAX). However, no code repository is provided, and the sigmoid intensity parameters and specific calibration choices are stated inline rather than in a structured format. The analytical framework (HJB, Riccati ODE, quadratic ansatz) is fully specified with equations (1)-(19), enabling independent reimplementation.