Numerical Comparison of Currency Price Prediction in Iran Using the Stochastic Black-Scholes Model with Different Noises
Keywords:
Mixed Noise, Lévy Noise, Numerical Simulation, Ito Stochastic Differential Equation, Stochastic Black-Scholes Model, Confidence Interval, EfficiencyAbstract
This study aims to compare the efficiency of mixed noise and Lévy noise as alternatives to Gaussian white noise in the stochastic Black–Scholes model for forecasting currency prices in Iran. The stochastic model under different noise processes was solved using the Euler–Maruyama numerical method. The model parameters were estimated from actual market data using the maximum likelihood estimation method, and a 95% confidence interval was calculated for the forecasted values. For this purpose, daily US dollar exchange-rate data covering the period from August 24 to December 13, 2024, were analyzed. The simulations were conducted using Maple software. To evaluate the accuracy and precision of the proposed approach, the US dollar exchange rate for December 22, 2024, was separately forecasted using the Euler–Maruyama method under Gaussian white noise, mixed noise, and Lévy noise. The corresponding simulation charts were also generated in Maple. The findings indicate that replacing Gaussian white noise and mixed noise with Lévy noise in the stochastic Black–Scholes model improves the efficiency of US dollar exchange-rate forecasting.
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Copyright (c) 2025 Sahebeh Aghababaeipour (Author); Ramzan Rezaeyan; Mohammad Ali Jafari, Bijan Rahmani Perchkolaei, Seyed Saleh Mohseni (Author)
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
