NUMERICAL SIMULATION OF FX RATES IN AN HESTON STOCHASTIC CORRELATION MODEL
Abstract
This paper proposes an enhanced approach to modeling and forecasting FX rates. One of the daunting problems in international mathematical finance is the weakness of existing theories to comprehensively model FX rates especially in periods of crisis. In this paper, we develop a new model that incorporates a stochastic volatility-stochastic interest rate-stochastic correlation structure and introduces a self-exciting jump in the variance of the FX process. Based on the $\alpha$-Heston model, the new model introduces an $\alpha$-root term and an $\alpha$-stable Lévy process in the variance of the FX rate. The inclusion of $\alpha$-parameter in the variance structure allows the model to capture both large and small fluctuations and extreme high peaks during crisis periods. We apply the model to the Cedi exchange rate against three major currencies that are exchanged widely in Ghana; the US dollar, the Great British Pounds Sterling and the Euro. The results show that there is significant evidence that the model can predict the Cedi’s performance against all three currencies. We conclude that the model is robust for implementation and forecasting currency rates.