The Model of Carbon Price Risk Prediction in European Markets Using Long Short-Term Memory- Geometric Brownian Motion

Accurate carbon market price prediction is one of the fundamentals in assessing the risks associated with carbon trading. Related studies on carbon price prediction were mainly focused on two major approaches: mathematical and/or machine learning models. Geometric Brownian Motion (GBM) is one of the mathematical models that can represent carbon price movements but requires modifying the sample size and the number of parameters for compiling the simulation numerically. Moreover, two critical parameters: (μ) mu and (σ) sigma need to be estimated to simulate the carbon price movements. In this study, the parameters μ and σ estimation are based on the average return value and standard deviation. However, if the carbon price movement is very volatile, we need to recognize its trend and characteristics by estimating the parameters precisely until there is no significant change (or stable) patterns. That is very expensive and may be intractable on high-dimensional data with less precise prediction. Therefore, we propose a hybrid model for carbon price prediction based on GBM with the parameter estimation using the Long Short-Term Memory (LSTM) model. The LSTM model was chosen because it has high accuracy in parameter estimation without losing the characteristics of the GBM stochastic model. Furthermore, Value at Risk (VaR) is utilized to measure the risk of carbon price volatility predictions. The simulation results showed the proposed model has higher prediction accuracy with a not-too-significant time difference, and the model is proven reliable in measuring future risks.