Financial Modelling

The Analytics Toolkit chapter taught you to measure a loss distribution — to read an EP curve and compute expected loss, VaR, and TVaR. But every metric there was computed on the subject loss distribution: the cedent’s raw losses, before any contract terms applied. This chapter is about where the distributions worth measuring actually come from, and how a contract reshapes them.

Financial modelling is the process of applying contract terms to subject losses to produce the reinsurer’s gross loss — the amount the reinsurer assumes. It is the same loss distribution from the toolkit, run through a contract.

Core thesis

A specific contract is a composition of a small set of common financial terms. Quota share, CatXoL, and AggXoL differ not in the terms they are built from, but in how those terms are composed.

The taxonomy of contract names hides how little actually varies underneath. The same handful of operations — filter, coverage period, occurrence excess, aggregate excess, scaling — reappear across every contract type. Once you see a contract as a pipeline of these terms, “advanced” structures stop being a separate subject: they are the same terms with more parameters, a few extra terms, or one contract feeding another.

How this chapter is organized

The chapter is a guide you read once, followed by a catalog you return to:

1. Dissecting a contract — Watch one CatXoL transform a single trial, one financial term at a time
2. Contracts as compositions — The algebra of terms, and how each contract type composes from the same blocks

Terms — each financial term in isolation: its formula, its effect on a trial, a runnable implementation, and its EP curve:

• Loss filter · Contract period · Scaling · Occurrence excess · Aggregate excess

Contracts — each canonical contract type, assembled from the terms:

• Quota share · Catastrophe excess of loss · Aggregate excess of loss

Then the topics that build on the catalog:

3. Financial perspectives — Subject, covered, gross, retained, and net — the same dollars seen from each side
4. Programs — Program structure, inuring, sourcing, and top & drop — how contracts combine and feed one another into a graph
5. Portfolios — The roll-up from a portfolio of contracts to one loss distribution: participation-then-sum, the portfolio EP curves, and why expected loss adds but tail risk diversifies

Putting everything learned so far to work — reading the portfolio’s risk posture, the marginal capital impact of a new contract, and retrocession — is taken up in the Applications chapter, where the roll-up is worked end to end on Helios Re’s portfolio.

By the end you will be able to:

• Decompose any contract into an ordered pipeline of financial terms
• Apply each term to trial loss data and read its effect on the EP curve
• Compose the canonical contract types — and their optional features — from the same blocks
• Reason about how contracts combine into programs and aggregate into a portfolio

This chapter assumes the Analytics Toolkit — trials, EP curves, and the core metrics — plus comfort reading short formulas and Python code alongside the prose. No actuarial background is assumed.

We continue with the Helios Re example. The SunCoast and Baltica trial loss data and the six base contracts from Foundations and the Analytics Toolkit are used throughout — the numbers recur from page to page.

The ending thesis carries into Applications, which puts the assembled toolkit to work on real business questions: a handful of operations on trial losses can express any contract ever written.