Narrow Results

We study models for electricity pricing and derivatives in the context of a deregulated market setting. In particular we value swing options, since these are the electricity derivatives that attract the most attention from market participants. These are American style options in that they allow for multiple exercises subject to a set of constraints on the consumption process. Through the use of a penalty function, we generalize the problem by allowing for the consumption restrictions to be broken. We characterize the price function as a stochastic optimal control problem, and show that the option is exercised in a bang-bang fashion. The value of the swing option is the solution to a backward stochastic differential equation, and we show how European calls, along with forward contracts, can be used to hedge them.

Swing options are a type of exotic financial derivative which generalize American options to allow for multiple early-exercise actions during the contract period. These contracts are widely traded in commodity and energy markets, but are often difficult to value using standard techniques due to their complexity and strong path-dependency. There are numerous interesting varieties of swing options, which differ in terms of their intermediate cash flows, and the constraints (both local and global) which they impose on early-exercise (swing) decisions. We introduce an efficient and general purpose transform-based method for pricing discrete and continuously monitored swing options under exponential Lévy models, which applies to contracts with fixed rights clauses, as well as recovery time delays between exercise. The approach combines dynamic programming with an efficient method for calculating the continuation value between monitoring dates, and applies generally to multiple early-exercise contracts, providing a unified framework for pricing a large class of exotic derivatives. Efficiency and accuracy of the method are supported by a series of numerical experiments which further provide benchmark prices for future research.