Similar to Darwin, we view variance as the true reality, while the average is a more abstract concept.
Embracing variance is challenging. Everyone wants to make money without risk, yet without volatility, there’s nothing to gain.
Yet, nearly everyone forecasts the next expected value, not the evolving variance. The same variance can yield different means, and the same expected value can result from distinct variances.
Our pricing model prioritizes capturing the variance first, and, given that variance, seeks to explain the expected value.
The model simultaneously addresses both means and dispersions in terms of explanatory variables. We employ a Generalized Additive Model (GAM) that further refines results by adhering to the most significant property: the inherent (or expected) variation within the data.
This approach ensures that:
- A unified statistical model is applied to estimate the total claim amount per policy within a policy year, accounting for the actual exposure of each policy.
- There are no separate models for the probability of a claim (frequency) and claim size—severity.
- Both mean and dispersion parameters are modeled in terms of risk factors. This facilitates rate making and estimation of the tail of the claim size distribution.
- Risk factors—explanatory variables—are incorporated parametrically or non-parametrically and may differ between frequency and severity given frequency models. For instance, in MTPL pricing, severity should not be influenced by the type of person, whereas frequency should account for it, as the exposure differs between legal and physical persons.
What it is important here, it’s the net variance that one can’t mitigate alone. Think about that and use it to YouR own advantage.