Valuation of electricity storage contracts based on the COS method

Valuation of electricity storage contracts based on the COS method: with underlying polynomial electricity prices

Boonstra, B.C. (TU Delft Electrical Engineering, Mathematics and Computer Science)

Oosterlee, C.W. (mentor)

Delft University of Technology

Applied Mathematics | Financial Engineering

2020-08-28

In this thesis we introduce valuation techniques to price electricity storage contracts, where the electricity prices follow a structural model based on polynomial processes. In particular we focus on a Fourier-based pricing method known as the COS method, which performs impressively to price the contracts accurately. We provide details on how to formalize an electricity storage contract, taking into account the physical limitations of an electricity storage and the operational constraints of the electricity grid. In addition to the electricity storage contract, other well-known options are being considered, such as the European option, Bermudan option and Bermudan option with multiple early-exercise rights, where the same asset price model is used based on polynomial processes. We propose an approximation of the characteristic function, so that the Fast Fourier Transform (FFT) can be applied to significantly reduce the computational complexity of the COS method, which is especially suitable for pricing Bermudan options and Bermudan options with multiple early-exercise rights. With the FFT-based algorithm, the computation time of the valuation of the discussed Bermudan-type options with the COS method is reduced from seconds to milliseconds. Furthermore, the Least Squares Monte Carlo (LSMC) method is presented to value the discussed financial derivatives and used to validate the results obtained with the COS method.

Electricity storage contract
Valuation
COS method
Polynomial processes
Least Squares Monte Carlo
Options
Electricity Prices
Energy markets
Characteristic function

http://resolver.tudelft.nl/uuid:bf0c3ee6-51c0-40aa-8a96-fc5e20ea1bdd

2020-08-20

Student theses

master thesis

© 2020 B.C. Boonstra