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

TL;DR

This paper extends the QLBS model to include a large trader whose transactions cause permanent impacts on exchange rates, using reinforcement learning to optimize hedging strategies with lower transaction costs.

Contribution

It introduces a reformulated QLBS model accounting for large trader impacts and develops a reinforcement learning approach for optimal hedging in this context.

Findings

Optimal hedging strategy with reduced transaction costs

Convergence of the hedging strategy to the trader's fair price

Quantification of exchange rate impacts by large trader transactions

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.