# Quantitative Energy Finance by Fred Espen Benth Valery A. Kholodnyi & Peter Laurence

Author:Fred Espen Benth, Valery A. Kholodnyi & Peter Laurence
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

4.6 Other Approaches

In the previous sections we have reviewed a number of mathematical techniques to price swing options. These techniques were split into two loose categories; first of them approaching the pricing problem from a purely probabilistic point of view whereas the second focusing on the interplay between stochastic control problems and partial differential equations. In addition to these, there is a selection of other techniques available in the literature. We review some of these techniques in this section.

The tree methods are a popular technique for option pricing—for an early study on multistrike path-dependent contingent claims, see [36]. In [25], the authors develop a trinomial-tree approach to swing option pricing. They use a well-known technique called backward induction to solve pricing problem. The induction starts on from the option’s expiration date and is done backwards in time in three dimensions: price, number of exercise rights left, and usage level. Assume that the holder has k exercise rights left. At each date, she chooses between exercising or waiting. Waiting corresponds to staying on the current tree associated with k remaining exercise rights whereas exercise corresponds to jumping down to the tree with k − 1 remaining exercise rights. So in fact, the solution is found not only on one but a forest of trees. Using this approach, the authors develop a numerical method for swing option pricing stemming from the trinomial tree building procedure of [23]. The approximating tree is built on the spot price process given as an Ornstein-Uhlenbeck process