FEATURES OF CONSTRUCTION AND SOFTWARE IMPLEMENTATION OF STOCHASTIC MODELS OF PRICE MOVEMENTS IN THE FOREX MARKET

Abstract

The article presents an in-depth comparative analysis of three stochastic models applied for forecasting exchange rates and quantitative risk assessment in the financial sector. The object of study is the EUR/USD currency pair, which serves as a key indicator of global macroeconomic trends, is characterized by high liquidity, and functions as a benchmark for a wide range of financial instruments. The models under consideration include geometric Brownian motion (GBM), the generalized autoregressive conditional heteroskedasticity model GARCH(1,1), and Merton’s jump–diffusion process, which represent different approaches to describing the dynamics of financial time series and capture both continuous and discrete characteristics of price changes.The research methodology involves the software implementation of models in the Python environment using the yfinance, numpy, arch, and matplotlib libraries. Daily EUR/USD quotes for the period 2015–2024 undergo standardized preprocessing: construction of logarithmic returns, stationarity testing (ADF), diagnostics of heavy tails and asymmetry, and outlier removal.The simulation experiment includes generating 1000 probabilistic trajectories at horizons of 1, 5, and 20 days, followed by computing accuracy metrics (MSE, MAE) and risk measures (VaR, CVaR) from the empirical predictive distribution.To visualize uncertainty, fan charts are constructed that display symmetry/asymmetry, the width of confidence intervals, and the overall character of risk dispersion, while also allowing for comparison between interval coverage and realized observations. Sensitivity analysis examines the influence of window length, innovation specification, jump intensity, and assumptions regarding drift and risk premium.Additional backtesting of risk forecasts is conducted: for VaR, the Kupiec unconditional coverage test and Christoffersen independence test are applied, enabling quantitative assessment of forecast reliability under both stable and turbulent conditions. Comparative results show that GBM provides a simple and computationally efficient framework for short- term forecasting but fails to reproduce volatility clustering and underestimates extreme events. The GARCH(1,1) model adequately models time-varying variance, improves risk evaluation accuracy, and reduces the frequency of VaR breaches, yet remains relatively insensitive to sudden news-driven jumps. Merton’s model, by combining Brownian and Poisson components, captures rare but significant price shifts and better reflects tail risks; the integration of continuous and discrete dynamics makes it particularly useful under abrupt regime shifts.It is concluded that integrating stochastic approaches with modern software tools establishes a reliable foundation for the development of adaptive currency-forecasting systems. The scientific novelty lies in a comprehensive comparison of three approaches with respect to their ability to reflect the specifics of the FX market, as well as in the practical validation of models on an extended time series covering nearly a decade with heterogeneous economic regimes. The practical significance is defined by the potential use of the results for algorithmic trading, currency risk hedging, strategic financial planning, and the design of integrated decision-support systems. In addition, directions for further research are outlined, including the expansion of the model class through hybridization of stochastic approaches with deep learning methods and the development of procedures for automatic model selection depending on prevailing market regimes.