What is a simple way to price a catastrophe excess of loss reinsurance program (Cat XL)? By simple we mean pricing a Cat XL with limited information. This paper presents pricing methods that only require the layer pricing of last year’s Cat XL program and do not require any catastrophe modelling output. The first method is to fit a power curve (i.e. a market curve) through the midpoints of the original Cat XL layers and then using that power curve to price the new program. This method has a history of actual use in the reinsurance market.
However, power curves have three key weaknesses and we therefore propose a new method. In this new method we propose a more sophisticated spline curve as the market curve, and unlike the power curve, layers are not represented by their midpoints, but rather by integrating from one endpoint to another. We show how this spline method resolves the three weaknesses of the power curve method.
Note: An Excel workbook accompanies this paper. There are tabs numbered from #1 to #10. We invite the reader to follow along in the workbook as instructed in the paper so as to increase his or her understanding of the methods. In the workbook, cells that serve as user inputs are highlighted in green. The parameters of market curves (power curves and splines) and the outputs of those market curves are shown in blue.
There are three graphs presented in the workbook that correspond with the three graphs presented in this paper. Should the reader wish to use his or her own Cat XL program in the workbook the axes of the graphs may need to be modified.
Keywords. Catastrophe, Excess of Loss, Reinsurance, Pricing
