| We develop a general numerical method for solving stochastic differential equations by constructing trinomial trees. The traditional trinomial tree is introduced and then a significant improvement is adapted to the method to create faster trees. The methods are illustrated by applying them to a class of mean reverting models suitable for modeling energy spot prices. We illustrate the models with crude oil, natural gas, and electricity data. The geometry of the trees is such that the futures prices match the expected future spot prices. This renders the probabilities risk neutral, in that investment opportunities in the energy market have no net present value. Hence, the trees can and are used to evaluate derivative securities. Numerical methods are developed to estimate the parameters in the mean reverting equations. |
