Modification of the Ornstein Uhlenbeck Process to Incorporate the Influence of Speculation on Volatility in Financial Markets

Abstract

Financial market participants often speculate on how markets would behave in the light of certain information at hand. This speculation contributes to volatility within the financial market and consequently, it makes the market unstable. The Ornstein Uhlenbeck (OU) model has intensively been used in modelling volatility, however, the contribution of speculation on volatility has not been studied in the OU model. Therefore, this study focuses on the modification of the OU model by incorporating a time dependent exponential function that caters for the contribution of speculation on volatility. The statistical properties of the Improved OU model are then studied and the results compared with properties of the OU model. NAD/USD exchange rate data is used to compare and validate the Improved model with the OU model. It was found that both the OU and Improved OU model had a similar expected price, while variance of price for the OU model stabilised upwards up to 16 and variance of price for the Improved OU model stabilised downwards up to 0.01. The variance of the Improved model was found to be much lower than that of the OU model. Additionally, it was found that the distribution of the forecasted price changed with different lead times for the OU model whereas, the distribution of the forecasted price for the Improved OU model did not change with different lead times. Thus, the OU model is a time specific model whereas the Improved OU model is an invariant time model. Consequently, the Improved OU model was found to be more efficient than the OU model.