# Real Option Valuation for Reserve Capacity

32 Pages Posted: 12 Oct 2014 Last revised: 3 Jul 2016

See all articles by John Moriarty

## John Moriarty

Queen Mary University of London - School of Mathematical Sciences

## Jan Palczewski

University of Leeds - School of Mathematics

Date Written: July 2, 2016

### Abstract

Motivated by the potential use of electricity storage to smooth fluctuations in supply and demand, we study the problem of writing American-type call options when the holder's exercise strategy is of threshold type (so that the time of exercise is known, but random). The writer must provide physical cover by buying and storing the asset {\em before} selling the option. We optimise the writer's strategy for a single option and for an infinite sequence of options, these two strategies being different. The latter is motivated by the lifetime valuation of an energy storage unit when used as reserve capacity in a power system. Our stochastic process is a Brownian motion representing the real-time system imbalance, and which we rescale to represent an imbalance price. The single option leads to an optimal stopping problem in which the principle of smooth fit may be violated and the stopping region may be disconnected. The lifetime analysis uses techniques and results for the single option to construct a certain fixed point characterising the value function.

Keywords: American option, real option, energy balancing, capacity market

JEL Classification: C61, G12

Suggested Citation

Moriarty, John and Palczewski, Jan, Real Option Valuation for Reserve Capacity (July 2, 2016). Available at SSRN: https://ssrn.com/abstract=2508258 or http://dx.doi.org/10.2139/ssrn.2508258