Potential Future Exposure Modelling For The Carbon Market

Within this thesis, we developed a model to facilitate the computation of Potential Future Exposure (PFE) at an individual deal level within the carbon market domain. In addition to other commodities such as oil, gas, and electricity, Shell engages in trading carbon allowances and credits, granting the entitlement to emit greenhouse gases or offset them. The imperative for a specialized PFE model tailored to the carbon markets is underscored by their expanding scale. We start this research by analysing the risk factors influencing carbon market prices and the methodologies available for their modelling. We favour directly modelling market prices rather than relying on alternative risk factors such as temperature, correlations with other commodities, or regulatory influences. The primary rationale behind this preference is the pursuit of a comprehensive PFE model that can be universally applied across all carbon markets. The chosen methodology for calculating PFE is the Monte Carlo simulation, as it accommodates the inclusion of deal optionalities, such as vanilla options. Subsequently, we examine carbon market data. Within one segment of the carbon markets, forward prices are available while in another segment, only spot prices are recorded within Shell. This dichotomy implies that for certain markets, it is feasible to directly model the forward curves, whereas for others, the forward prices must be derived from simulated spot prices. Despite the consideration and testing of various forward curve models, we decide to uniformly model forward curves in all carbon markets by simulating the spot price and extrapolating this value with a fixed percentage to establish a linear forward curve. This determination stems from our principal component analysis, revealing that spot prices contribute to more than 96% of the price variance across all carbon markets. Following the assessment of stochastic spot price models on historical data, the Geometric Brownian Motion, Merton Jump Diffusion Model, and the GBM-hypsec model (where a normal random variable is replaced by a hyperbolic secant random variable in the GBM) emerged as the most suitable options. We developed a PFE model in Python, providing users with the capability to employ these three stochastic models within the price simulation engine. This model is specifically designed for a forward sale deal, involving the receipt of a predetermined quantity of carbon allowances or credits in the future in exchange for an upfront lump sum payment, potentially in conjunction with vanilla (put/call) options. Additionally, the model accommodates swap deals, wherein one category of allowance/credit is exchanged for another