Currents Beneath Stability: A Stochastic Framework for Exchange Rate Instability Using Kramers Moyal Expansion

TL;DR

This paper develops a stochastic modeling framework using Kramers-Moyal expansion and Fokker-Planck formalism to analyze and detect regime shifts in exchange rate dynamics, with applications to USD in Iran, Turkey, and Sri Lanka.

Contribution

It introduces a novel application of stochastic differential equations to model exchange rate instability and detect regime shifts linked to political and economic events.

Findings

Confirmed Markovian nature of exchange rate fluctuations

Identified regime shifts correlating with major events

Revealed stabilizing and nonlinear volatility effects

Abstract

Understanding the stochastic behavior of currency exchange rates is critical for assessing financial stability and anticipating market transitions. In this study, we investigate the empirical dynamics of the USD exchange rate in three economies, including Iran, Turkey, and Sri Lanka, through the lens of the Kramers-Moyal expansion and Fokker-Planck formalism. Using log-return data, we confirm the Markovian nature of the exchange rate fluctuations, enabling us to model the system with a second-order Fokker-Planck equation. The inferred Langevin coefficients reveal a stabilizing linear drift and a nonlinear, return-dependent diffusion term, reflecting both regulatory effects and underlying volatility. A rolling-window estimation of these coefficients, paired with structural breakpoint detection, uncovers regime shifts that align with major political and economic events, offering insight into the hidden dynamics of currency instability. This framework provides a robust foundation for detecting latent transitions and modeling risk in complex financial systems.