The project was focused on developing a simulation model of the underwriting cycle for Property and Liability lines based on US data. Figure 1 shows the underwriting cycles for different product lines in the USA for the period 1993-2007: the Economic Loss Ratio (ELR) is a reciprocal measure of price used in many academic papers dealing with the underwriting cycle and plotted on a yearly basis in Figure 1. The ELR is calculated by dividing the discounted Loss Ratio by (1 – Expense Ratio). The main objective was to review the academic literature and identify a model that determines the factors influencing the underwriting cycle as well as predicting the next few years’ behaviour.

The approach

The first step was to review the academic publications that attempt to model the underwriting cycle and replicate some of them using currently available data for the USA. The second step was to decide on which factors to include into the model, for example which interest rate to use, and to introduce new significant variables not mentioned in the existing literature. The last step was to move from aggregate industry data to by-line data (i.e. motor insurance, medical malpractice etc.). For the aggregate industry data the classical linear regression model is used, and for the by-line analysis panel data econometrics is used. Computational results are for the USA (for the period 1985-2007) as well as the UK (for the period 1985-2004). The model is implemented in R and the simulation model in Igloo Professional. The R code manipulates the industry and by line data, runs the linear regression model and estimates the panel model.

Figure 2 shows the computational results for the USA: the red lines are the original annual ELRs (Economic Loss Ratio) for different lines and the blue lines are the estimates gained from our model. The black line at the end of the fitted model at year 22 represents the forecasted ELR for the next year using the coefficients from our model and currently available model variables. For both the USA and UK case the models fitted the data very well.