The QLBS Model within the presence of feedback loops through the impacts of a large trader

Paper: arXiv 2311.06790

Authors: Ahmet Umur Özsoy, Ömür Uğur

Abstract

We extend the QLBS model by reformulating via considering a large trader whose transactions leave a permanent impact on the evolution of the exchange rate process and therefore affect the price of contingent claims on such processes. Through a hypothetical limit order book we quantify the exchange rate altered by such transactions. We therefore define the quoted exchange rate process, for which we assume the existence of a postulated hedging strategy. Given the quoted exchange rate and postulated hedging strategy, we find an optimal hedging strategy through batch-mode reinforcement learning given the trader alters the course of the exchange rate process. We assume that the trader has its own concept of fair price and we define our problem as finding the hedging strategy with much lower transaction costs yet delivering a price that well converges to the fair price of the trader. We show our contribution results in an optimal hedging strategy with much lower transaction costs and convergence to the fair price is obtained assuming sensible parameters.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 4.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a strong theoretical extension of the QLBS model using Q-learning and market impact dynamics from a large trader. However, it relies primarily on hypothetical limit order book parameters and simulated dynamics rather than rigorous empirical backtesting on real tick data.

Research Flowchart

  flowchart TD
    A[Goal: Optimal FX Hedging & Fair Pricing<br/>with Large Trader Market Impact] --> B[Input: Limit Order Book &<br/>Quoted Exchange Rate Process]
    B --> C[Formulate QLBS Extension:<br/>Model Feedback Loops & Permanent Impact]
    C --> D[Postulate Initial Hedging Strategy<br/>& Define Trader's Fair Price]
    D --> E[Batch-Mode Reinforcement Learning:<br/>Optimize Strategy to Reduce Transaction Costs]
    E --> F[Outcome: Optimal Hedging Strategy<br/>with Lower Costs & Convergence to Fair Price]