Jump Diffusion and Brownian Motion for Examining BRIC Countries Carry

We examine the robustness of the Jump Diffusion Model relative to the Geometric Brownian Motion in forecasting the Japanese Yen carry trade daily returns for the BRIC countries and three bellwether currency pairs GBP/JPY, EUR/JPY, and PLN/JPY during the January 2, 2012 - July 31, 2026, sample period. We include the interest rate return, specifically, the interest earned from the (long position) component of the FX Carry trade in arriving at the daily cumulative carry trade returns. Focusing on the uncovered interest rate parity (UIRP) condition, we find that Jump Diffusion outperforms Geometric Brownian Motion JPY carry trade. However, the Geometric Brownian Motion fits the daily time series data better on some FX Carry trading strategies. The anticipated accuracy of both models is better under quantitative easing relative to quantitative tightening monetary policies.