The objective of this research is to model the behavior of oil returns. The volatility of oil returns is described through a TGARCH process. Conditional probability jumps are incorporated through uniform, double exponential and normal jump intensity distributions. We found that the volatility of oil returns follows the stylized facts of leptokurtosis, leverage effect and volatility clustering. The abnormal information that causes the jumps, can cause another type of unexpected changes in the following period and the intensity of the jumps has a negative effect on the probability of jumps in the next period. The dynamic model proposed can be extended to other markets and to multivariate time series modeling considering the dependence among the markets’ returns. The main contribution of this work is the estimation of the conditional probability of jumps depending on the previous behavior leading to a better description of the stochastic dynamics of crude oil prices. This will be useful for making better decisions regarding oil as an underlying asset in derivatives or in the formulation of better public policies.
Highly efficient Shannon wavelet-based pricing of power options under the double exponential jump framework with stochastic jump intensity and volatility
