Jump-diffusion modeling in emission markets through an integro-differential equation

In this thesis, will be explored how emission allowance prices evolve in carbon markets, using mathematical models that account for both gradual changes and sudden shocks. Inspired by the work of Borovkov et al., the study replicates the results based on a jump-diffusion model with standard normally distributed jumps. Then it goes further by testing two alternative models, the Double Exponential and CGMYdistributions, that aimtobetter reflect the real behavior of the market, particularly in situations of extreme volatility. The model is solved numerically using the finite difference method, with all simulations implemented in Python. By comparing the effects of different jump distributions, the thesis provides insights into how these models can help price emission-related financial derivatives more accurately and support better decision-making in systems like the EU Emissions Trading Scheme (EU ETS).