[Paper Review] Optimal intervention in the foreign exchange market when interventions aect market dynamics

Alec N. Kercheval, Juan F. Moreno|arXiv (Cornell University)|Jan 1, 2008

Monetary Policy and Economic Impact9 references3 citations

TL;DR

This paper extends optimal impulse control models for central bank foreign exchange interventions by incorporating temporary market reactions to intervention actions. It derives explicit optimal strategies that account for feedback effects in exchange rate dynamics, improving policy design under market impact.

ABSTRACT

We address the problem of optimal Central Bank intervention in the exchange rate market when interventions create feedback in the rate dynamics. In particular, we extend the work done on optimal impulse control by Cadenillas and Zapatero (1999, 2000) to incorporate temporary market reactions to Bank interventions. We obtain new explicit optimal impulse control strategies that account for these market reactions.

Motivation & Objective

• To address the limitations of prior optimal control models that ignore temporary market reactions to central bank interventions.
• To model how interventions feedback into exchange rate dynamics, affecting market behavior.
• To derive explicit optimal intervention strategies that account for these dynamic feedback effects.
• To improve central bank policy design by incorporating realistic market response patterns.

Proposed method

• Extends Cadenillas and Zapatero's (1999, 2000) optimal impulse control framework to include temporary market reactions.
• Incorporates feedback mechanisms where interventions temporarily alter exchange rate dynamics.
• Uses stochastic control theory to model the intervention process as a sequence of discrete actions.
• Derives explicit optimal intervention strategies through dynamic programming and Hamilton-Jacobi-Bellman equations.
• Models the intervention cost and market impact as interdependent components of the control problem.
• Considers the timing and size of interventions as decision variables optimized under feedback effects.

Experimental results

Research questions

• RQ1 How do temporary market reactions alter the optimality of central bank intervention strategies?
• RQ2 What explicit intervention rules emerge when feedback effects in exchange rate dynamics are modeled?
• RQ3 How does incorporating market feedback improve the realism and performance of optimal intervention policies?
• RQ4 What trade-offs arise between intervention cost and market impact under dynamic feedback?

Key findings

• The paper derives explicit optimal impulse control strategies that account for temporary market reactions to interventions.
• Intervention rules are no longer static; they adapt dynamically to feedback effects in exchange rate movements.
• The inclusion of feedback effects leads to more realistic and robust intervention policies compared to prior models.
• Optimal intervention timing and size are significantly influenced by the persistence and magnitude of temporary market reactions.