This master’s thesis explores the energy consumption involved in numerical pricing of financialderivatives using a hybrid numerical method that combines Radial Basis Function GeneratedFinite Difference (RBF-FD) and the Finite Difference Method (FDM). The proposed model discretizes the computational domain predominantly with FDM, while regions requiring higheraccuracy are handled using RBF-FD. The model problem considered is a two-dimensional European option, which features a discontinuity in its first derivative at maturity.

To evaluate the energy efficiency of the approach, energy consumption is measured usingIntel’s Model-Specific Registers (MSR) through the Running Average Power Limit (RAPL) interface. This enables a detailed analysis of the trade-offs between computational performanceand energy efficiency. The main objectives of this thesis include:

• Integration of mixed precision into the finite difference scheme within the hybrid solver.

• Measuring energy consumption on the Rackham cluster at UPPMAX.

• Evaluation of performance and energy consumption of the mixed-precision hybrid solver.

Numerical results demonstrate that the mixed precision implementation achieves sufficientaccuracy for solving the problem. However, there remains room for further optimization of itscomputational performance and energy efficiency within the MATLAB framework. Thesefindings suggest that while mixed precision hybrid methods are viable for addressing complex numerical problems, alternative computational platforms or implementations may be necessaryto fully exploit their potential.

The energy measurement process is demonstrated to be both stable and reliable, reinforcingthe robustness of the measurement technique and ensuring the validity of the results. Furthermore, the analysis highlights a strong correlation between energy efficiency andcomputational time. This shows that direct methods exhibit energy consumption advantages forsmaller-scale applications, whereas iterative methods prove to be more efficient in large-scale settings.