Energy markets are characterized by unique features such as seasonality, mean reversion, and sudden price spikes, which make the valuation of related derivatives considerably more challenging than in traditional financial markets. This thesis investigates the use of the COS method, a Fourier-based numerical technique, for the efficient valuation of energy derivatives within a Markov-modulated framework.

The study begins with energy quanto options, whose payoff depends on two correlated underlyings incorporating jumps and regime-switching dynamics. By deriving the characteristic functions for two benchmark models and implementing the COS method, the results demonstrate high accuracy and significant computational speed-ups compared to FFT- and Monte Carlo-based benchmarks.

The research work then extends to electricity storage contracts, which feature early-exercise opportunities and operational constraints. In line with the methodology presented by [1], this section replicates their integration of the COS method into a dynamic programming framework to evaluate the option values across multiple contract types and volatility regimes. The obtained prices fall within the confidence intervals of the LSMC benchmark, confirming the robustness of the COS approach in handling path-dependent and constrained problems.

Finally, the pricing framework is generalized to electricity storage under a two-state Markov-modulated model, to better capture the behavior of electricity prices. The extended COS-based algorithm accurately reproduces complex probability densities and achieves stable convergence of the prices while maintaining high computational efficiency even under this more complex setting.

In conclusion, this thesis demonstrates that the COS method is a powerful and computationally efficient alternative to stochastic simulation methods for pricing energy derivatives. It is capable of handling jump dynamics, regime switching, early-exercise features and operational constraints, highlighting its potential for broader applications in energy finance.

[1] Boris C Boonstra and Cornelis W Oosterlee. “Valuation of electricity storage contracts using the COS method”. In: Applied Mathematics and Computation 410 (2021), p. 126416