# The Role of Data-Driven Methodologies in Weather Index Insurance
## 4 Methodology
### Data
#### 4.1.6 Result Validation  
In addition to assessing the quality of a model, based on performance metrics, it is possible to assess the utility of the model, i.e., the economic value it brings to the end user. In fact, a measure of value is even more important than a measure of quality since users are primarily concerned with the estimated benefit that models can bring in the context of the problem [31]. To evaluate the usefulness of the implemented models, we follow the methodology implemented by [PERSON] [31] which is summarized below. Table 3 shows the frequencies of the four possible combinations of predicted and occurring events. Each component of the table has an associated cost, which can be expressed in the form of a cost matrix (Table 4). The average cost of using a certain predictive system can be obtained by multiplying the relative frequencies and associated costs. \[E_{sistema}=\frac{a}{n}E_{a}+\frac{b}{n}E_{b}+\frac{c}{n}E_{c}+\frac{d}{n}E_{d} \tag{12}\]  
Although this equation allows researchers to calculate the average value, it is also useful to calculate a measure of the benefit obtained by using the predictive system. Thus, a reference or base system is defined, for which a system that never predicts a loss event (flood) is assumed. In this case, the average cost is given by  
\[E_{base}=sE_{c}+(1-s)E_{d} \tag{13}\]  
where  
\[s=(a+c)/n \tag{14}\]  
The value is then defined as  
\[V=E_{base}-E_{system} \tag{15}\]  
In addition, the average cost associated with a perfect forecasting system, for which the predictions and the observed events always agree, is defined. The cost of this system is given by  
\[E_{perfect}=sE_{a}+(1-s)E_{d} \tag{16}\] \begin{table}
\begin{tabular}{c c c} \hline \hline  & \multicolumn{2}{c}{**Observed**} \\ \hline
**Prediction** & **Yes** & **No** \\ \hline Yes & \(E_{a}\) & \(E_{b}\) \\ No & \(E_{c}\) & \(E_{d}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Event costs for each case. \begin{table}
\begin{tabular}{c c c} \hline \hline  & \multicolumn{2}{c}{**Observed**} \\ \hline
**Prediction** & **Yes** & **No** \\ \hline Yes & a & b \\ No & c & d \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Event frequency for each case. which corresponds to the upper bound on the maximum value that can be obtained from a system. By presenting the predictions in probability form, the end user is faced with the possibility of selecting the cut-off point \(q\) that maximizes the value they can obtain from the system. Varying the cut-off point from 0 to 1 allows a sequence of values \(V(q)\) to be computed, from which the optimal decision can be found. The model is evaluated from the perspective of two users of a hypothetical parametric insurance product. This includes the policyholder and the insurer. The cost matrices associated with each of the parties are then defined. For the insured party, in this case, the Antioquia region, \(E_{a}\) is defined as the expected indemnity in the event of a loss event (flood). It is assumed that the indemnity corresponds to the expectations of the department, so there is no net gain or loss for the insured party. The premium to be paid by the department is defined as follows:  
\[E_{p}(q)=\frac{a(q)+b(q)}{n}E_{a}m \tag{17}\]  
where \(m\) corresponds to the insurer's relative profit margin (\(m>1\)). Finally, assume that \(E_{n}>E_{a}\) represents the losses incurred by the department in case a loss event occurs but no indemnity is generated. Now, the costs of the second party, the insurer, are defined. Assume that \(E_{c}\) corresponds to the operational costs related to administrative actions each time an indemnity is generated, \(E_{r}\) corresponds to the reputations and model recalibration costs generated each time an indemnity is generated but no event occurred, and \(E_{l}\) is the reputation cost and the potential loss of a customer each time the model fails to generate an indemnity when a loss event occurs.