# Financial Modelling

> How reinsurance contracts transform loss distributions: the financial terms that turn a cedent's subject loss into gross loss, and how they compose.

Source: https://reinsurance.dev/financial-modelling/

The [Analytics Toolkit](https://reinsurance.dev/toolkit/) chapter taught you to measure a loss distribution: to read an [exceedance probability (EP) curve](https://reinsurance.dev/toolkit/distributions/) and compute [expected loss, Value at Risk (VaR), and Tail Value at Risk (TVaR)](https://reinsurance.dev/toolkit/metrics/). But every metric there was computed on the **[subject loss](https://reinsurance.dev/glossary/#subject-loss)** distribution: the losses the cedent presents to the contract, before any term applies. This chapter is about where a reinsurer's loss distributions come from, and how a contract reshapes them.

**[Financial modelling](https://reinsurance.dev/glossary/#financial-modelling)** is the process of applying contract terms to subject losses to produce the reinsurer's **[gross loss](https://reinsurance.dev/glossary/#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.[^composition] Quota share, [catastrophe excess of loss (CatXoL)](https://reinsurance.dev/glossary/#catxol-catastrophe-excess-of-loss), and [aggregate excess of loss (AggXoL)](https://reinsurance.dev/glossary/#aggxol-aggregate-excess-of-loss) differ not in the terms they are built from, but in [how those terms are composed](https://reinsurance.dev/financial-modelling/dissection/).

The taxonomy of contract names hides how little varies underneath. The same handful of operations (loss filter, contract 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 depending on another. Contract 1, dissected on the next page, is four of them in sequence, reading a [year event loss table (YELT)](https://reinsurance.dev/glossary/#yelt-year-event-loss-table) in and writing one out:

```mermaid
graph TB
    S[Subject loss<br/>SunCoast's YELT]:::Losses --> F[Loss filter<br/>Florida hurricane]:::Contract
    F --> P[Contract period<br/>calendar 2024]:::Contract
    P --> O[Occurrence excess<br/>$30M xs $10M]:::Contract
    O --> A[Aggregate excess<br/>$60M — one reinstatement]:::Contract
    A --> G[Gross loss<br/>Contract 1's YELT at 100%]:::Metric

    classDef Losses fill:#F5CEBC,stroke:#B16C4B,stroke-width:1.5px,color:#2B2620
    classDef Contract fill:#BFDBF8,stroke:#4F84BA,stroke-width:1.5px,color:#2B2620
    classDef Metric fill:#BDE2CB,stroke:#459269,stroke-width:1.5px,color:#2B2620
```

## How this chapter is organised

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

- [**Dissecting a contract**](https://reinsurance.dev/financial-modelling/dissection/): Watch one CatXoL transform a single trial, one financial term at a time
- [**Contracts as compositions**](https://reinsurance.dev/financial-modelling/composition/): The algebra of terms, and how each contract type composes from the same blocks

[**Term catalog**](https://reinsurance.dev/financial-modelling/terms/), each financial term in isolation: its formula, its effect on a trial, a runnable implementation, and its EP curve; the catalog page itself is the one-row-per-term reference:

- [Loss filter](https://reinsurance.dev/financial-modelling/terms/filter/) · [Contract period](https://reinsurance.dev/financial-modelling/terms/contract-period/) · [Scaling](https://reinsurance.dev/financial-modelling/terms/scaling/) · [Occurrence excess](https://reinsurance.dev/financial-modelling/terms/occurrence-excess/) · [Aggregate excess](https://reinsurance.dev/financial-modelling/terms/aggregate-excess/)

[**Contract catalog**](https://reinsurance.dev/financial-modelling/contracts/), each canonical contract type, assembled from the terms:

- [Quota share](https://reinsurance.dev/financial-modelling/contracts/quota-share/) · [Catastrophe excess of loss](https://reinsurance.dev/financial-modelling/contracts/catxol/) · [Aggregate excess of loss](https://reinsurance.dev/financial-modelling/contracts/aggxol/)

Then the topics that build on the catalog:

- [**Financial perspectives**](https://reinsurance.dev/financial-modelling/perspectives/): Subject, covered, gross, retained, and net (the same dollars seen from each side)
- [**Beyond loss**](https://reinsurance.dev/financial-modelling/beyond-loss/): The flows a contract generates besides loss, each kept as its own table on the occurrence key; the first entry is [reinstatement premium](https://reinsurance.dev/financial-modelling/beyond-loss/reinstatement-premium/), the premium a paid reinstatement earns and what it does to a layer's capital
- [**Programs**](https://reinsurance.dev/financial-modelling/programs/): Program structure and inuring, where one contract's recoveries reduce another's subject loss and the contracts form a graph; forwarding and top & drop are introduced, not covered
- [**Portfolios**](https://reinsurance.dev/financial-modelling/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

The [Applications](https://reinsurance.dev/applications/) chapter reads the portfolio's risk posture as a business position and works the roll-up end to end on Caldera Re's portfolio.

By the end, you will be able to:

- Decompose the core property-cat contracts into an ordered composition 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 roll up into one portfolio loss distribution

This chapter assumes the [Analytics Toolkit](https://reinsurance.dev/toolkit/) ([trials](https://reinsurance.dev/toolkit/trials/), [EP curves](https://reinsurance.dev/toolkit/distributions/), and the [core metrics](https://reinsurance.dev/toolkit/metrics/)) plus comfort reading short formulas and Python code alongside the text. No actuarial background is assumed.

The conventions this chapter introduces are indexed on [Scope, conventions & assumptions](https://reinsurance.dev/conventions/).

We continue with the **[Caldera Re](https://reinsurance.dev/caldera-re/)** example. The six base contracts introduced in [Foundations](https://reinsurance.dev/foundations/) run throughout, on the SunCoast and Baltica trial loss data from the [Caldera Re dataset](https://reinsurance.dev/caldera-re/#portfolio). The numbers recur from page to page.

The chapter ends where [Applications](https://reinsurance.dev/applications/) begins, putting the terms, contracts, and portfolio roll-up to work on real business questions: **a handful of operations on trial losses can express the loss side of the core property-cat structures (quota share, catastrophe excess of loss, aggregate excess of loss) and of programs and portfolios built from them; other structures add terms to the catalog.**

[^composition]: Aman Bahl, Oliver Baltzer, Andrew Rau-Chaplin, and Blesson Varghese, ["Parallel Simulations for Analysing Portfolios of Catastrophic Event Risk"](https://arxiv.org/abs/1308.2066), Workshop at SC12, 2012 (co-authored by this site's author), whose layer model parameterises a layer by four financial terms: occurrence retention, occurrence limit, aggregate retention, and aggregate limit. Oasis LMF, [*Oasis Financial Module*](https://oasislmf.org/application/files/2016/1832/6318/OasisFinancialModule_v2020.pdf), Peter Taylor and Johanna Carter, 2020, likewise represents a contract as calculation rules plus "the specific financial terms such as deductibles and limits". Neither source makes the claim this chapter closes on; that claim is this site's.