Foreign exchange (FOREX) markets are the world's largest and most complex financial markets, characterized by high volatility and non-linearity. Accurately predicting future currency prices is crucial for both individuals and financial institutions. While various models, primarily using statistical methods such as Monte Carlo algorithms, have been developed, their accuracy, especially with smaller sample sizes, remains a challenge. This study addresses this limitation by introducing AFQMC as a novel approach to improve the precision of FOREX market models, particularly in simulating speculative attack scenarios. The increased accuracy in forecasting, especially during periods of high volatility, offers significant advantages for risk management and informed decision-making in the financial sector. Recent economic events, including the 2020 market collapse and the COVID-19 pandemic, have underscored the critical need for robust forecasting tools to navigate the uncertainties of the FOREX market.

Existing research on FOREX market prediction has explored numerous methods, including statistical techniques (regression, decision trees, support vector regression, fuzzy systems), and more recently, deep learning approaches (neural networks, LSTM). While some studies have used Monte Carlo simulations, the application of quantum-enhanced methods like AFQMC remains largely unexplored. Studies using statistical methods have shown varying degrees of success, with accuracy ranging from approximately 70% to 90% depending on the methodology and sample size. Neural network approaches have also demonstrated promising results, but their accuracy can still be improved. This study aims to fill this gap by introducing AFQMC, a novel quantum-enhanced method, and comparing it to traditional Monte Carlo methods for increased precision in FOREX market prediction.

The study uses daily closing data for USD/EUR and USD/JPY exchange rates from 2013 to 2021 obtained from Yahoo Finance. Macroeconomic indicators (short-term interest rates, international reserves, M1, commodity prices, 10-year government bond yields) sourced from FRED, Eurostat, World Bank Open Data, and Bank of Japan's statistics are also incorporated. Three Monte Carlo techniques are compared: Markov Chain Monte Carlo (MCMC), Sequential Monte Carlo (SMC), and the novel AFQMC. Several exchange rate dynamics models are estimated, including uncovered interest rate parity (UIRP), purchasing power parity (PPP), behavioral equilibrium exchange rate (BEER), sticky-price monetary (SPM), and Taylor rule fundamentals models. A speculative attack model (Eichengreen et al., 1994) and its second-generation variant (Flood and Marion, 1997) are also included to simulate stress scenarios. Model performance is evaluated using classification accuracy (in-sample and out-of-sample), RMSE, and MAPE. The Gelman-Rubin test assesses the convergence of Markov chains. The Diebold-Mariano test compares the forecasting accuracy of different methods. The study utilizes two Intel Core I7-6500U quad-core processors and MATLAB (R2019b) for implementation, with 500 computing runs conducted for each model estimation.

The results show that AFQMC consistently outperforms both MCMC and SMC across all models and sample sizes (200 and 500 observations). For the USD/EUR exchange rate, out-of-sample classification accuracy exceeds 87% for AFQMC, compared to 80-85% for MCMC and SMC. The RMSE and MAPE values are also significantly lower for AFQMC. Similar trends are observed for the USD/JPY exchange rate, with out-of-sample accuracy exceeding 90% for AFQMC. The Diebold-Mariano test confirms the statistical significance of the superior performance of AFQMC over MCMC and SMC in most cases. The AFQMC method also shows a significant reduction in computation time compared to the other methods. The accuracy achieved by the AFQMC method surpasses those reported in previous literature which used statistical, machine learning (neural networks, Support Vector Machines, Random Forest), or traditional Monte Carlo methods.

The superior performance of AFQMC in predicting FOREX exchange rates demonstrates the potential of quantum-enhanced Monte Carlo methods for financial modeling. The higher accuracy and lower error rates, particularly with smaller sample sizes, suggest that AFQMC can provide more robust and reliable forecasts, especially during periods of market instability. The significant improvement in accuracy compared to existing methods, including both statistical and deep learning approaches, highlights the potential of quantum computing for addressing challenges in financial econometrics. The faster computation times also make AFQMC a more practical tool for real-time applications.

This study demonstrates the efficacy of AFQMC for estimating FOREX market models, particularly in simulating speculative attacks. AFQMC significantly improves accuracy and reduces computation time compared to traditional Monte Carlo methods. This research provides valuable insights for risk management, policy-making, and trading strategies. Future research could explore the application of AFQMC to other financial markets and incorporate additional macroeconomic indicators to further refine model accuracy.

The study focuses on two currency pairs (USD/EUR and USD/JPY) and a specific time period. The generalizability of the findings to other currencies or time periods requires further investigation. Also, the study does not incorporate the simulations of these Monte Carlo models into trading models for a market strategies simulation, which is an interesting future line of research.