Exchange Rate Dynamics

Currents Beneath Stability: A Stochastic Framework for Exchange Rate Instability Using Kramers Moyal Expansion ArXiv ID: 2507.01989 “View on arXiv” Authors: Yazdan Babazadeh Maghsoodlo, Amin Safaeesirat 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. ...

Automated Market Making: the case of Pegged Assets ArXiv ID: 2411.08145 “View on arXiv” Authors: Unknown Abstract In this paper, we introduce a novel framework to model the exchange rate dynamics between two intrinsically linked cryptoassets, such as stablecoins pegged to the same fiat currency or a liquid staking token and its associated native token. Our approach employs multi-level nested Ornstein-Uhlenbeck (OU) processes, for which we derive key properties and develop calibration and filtering techniques. Then, we design an automated market maker (AMM) model specifically tailored for the swapping of closely related cryptoassets. Distinct from existing models, our AMM leverages the unique exchange rate dynamics provided by the multi-level nested OU processes, enabling more precise risk management and enhanced liquidity provision. We validate the model through numerical simulations using real-world data for the USDC/USDT and wstETH/WETH pairs, demonstrating that it consistently yields efficient quotes. This approach offers significant potential to improve liquidity in markets for pegged assets. ...