This thesis investigates the estimation of option-implied probability density functions for inflation using inflation options, focusing not only on the expected value but the whole distribution. The aim is to identify the most effective method for measuring the market expectation of future inflation. The research explores both parametric and non-parametric approaches for deriving these density functions from inflation option prices. Methodologies include parametric models such as expansion, generalised distribution, and mixture methods, alongside non-parametric techniques using Breeden and Litzenberger’s result, such as curve-fitting and kernel methods. Implementing these methods involved analysing inflation option data sourced from the BVOL Bloomberg database, specifically for Harmonised Index of Consumer Prices excluding Tobacco (HICPxT) options from January 1, 2013. The study employed Shimko’s method, various spline methods, the Delta method, and Kernel method, assessing their effectiveness and challenges. Results reveal diverse implications for each method. Visual comparisons showcase the varying outcomes of the implemented methods, Likelihood-based assessments present a more numerical approach benefiting the Delta and Kernel methods due to higher scores and fewer negative likelihoods. Conclusions suggest that while multiple methods offer insights into inflation prediction, the Kernel method shows promise in its reliability while the Delta method scores highest in the numerical methods. However, challenges in accurately modelling extreme values and tail behaviours persist across methodologies. Recommendations for further research involve addressing these limitations and exploring enhancements to refine inflation prediction models.F

This thesis developed a computer powered simulation study of the divisible sandpile model. It introduces a constant to a widely used formula to generate sandpiles. This constant can be used to study the convergence characteristics of sandpiles. In this thesis it is shown that the introduced factor increases the speed of convergence while it no longer stabilizes in the all-1-configuration. While one should be careful with using this constant as it does not work for every distribution, it does speed up the stabilization significantly. There is also a positive correlation found between the constant and the amount of nodes that remain lower than 1 in the stable state.