Abstract:
The main objective of this work is to determine the most appropriate model for forecasting the daily exchange rate of the Sri Lanka Rupee (LKR) against the United States Dollar (USD) among the geometric Brownian motion (GBM) and three selected stochastic differential equations (SDEs) used in stochastic analysis of financial markets. As a first step, we obtained the exchange rate data of LKR against USD throughout the day from the http://www.Xrates.com website and studied the behavioral pattern. We observed compact fluctuations in exchange rates for 24 hours on one day and large fluctuations on another day. Thus, we identified three types of fluctuations in the 24-hour exchange rate data, namely, small, intermediate, and large. Then, hourly exchange rates were obtained for these three types of fluctuations, that is, on 2021.04.26 for small, on 2021.03.11 for intermediate, and on 2021.04.05 for large. We calculated the drift and volatility parameters for these three types using corresponding exchange rate values obtained for the small, intermediate, and large, respectively.
