Capital Modelling

An insurer's internal model for Solvency II capital is among the most complex and consequential models in financial services. It determines how much capital the firm must hold, which directly affects shareholder returns, pricing competitiveness, and strategic capacity. Yet a major model change can take eighteen months or longer to gain PRA approval. When the risk environment moves faster than the model change cycle, capital modelling becomes a constraint on the business it is meant to protect.

What is capital modelling?

Capital modelling in insurance is the process of quantifying the capital required to absorb losses over a defined time horizon at a specified confidence level. Under Solvency II, insurers calculate a Solvency Capital Requirement (SCR) that represents the funds needed to survive a one-in-200-year loss event. Firms can use the standard formula prescribed by regulators or, with supervisory approval, develop an internal model tailored to their specific risk profile.

Internal models are substantially more complex than the standard formula. They simulate the firm's entire risk landscape: catastrophe risk, reserve risk, premium risk, market risk, credit risk, and operational risk, including the dependencies between them. A single model run may simulate millions of scenarios, each producing a full balance sheet outcome. The SCR is derived from the tail of this simulated distribution. The 99.5th percentile loss determines the capital the firm must hold.

The governance requirements are formidable. The PRA's internal model approval process requires firms to demonstrate that the model is used in decision-making (the "use test"), that the assumptions are justified and documented, that the model is validated independently, and that the data feeding the model meets quality standards. Major model changes require pre-approval, and the PRA's review cycle for major changes typically runs twelve to eighteen months. Minor changes follow a lighter process but still require notification and documentation.

The landscape

The PRA's SS1/23 on model risk management has broadened the scope of model governance beyond Solvency II internal models to encompass all material models, including AI and machine learning models used in risk assessment and pricing. For capital modelling teams, this means that any AI components incorporated into the internal model must meet the same governance, validation, and documentation standards as traditional model components. The bar is high and the regulatory tolerance for experimentation is low.

EIOPA's review of Solvency II, implemented through amendments taking effect from 2026, adjusts the standard formula calibrations and introduces changes to the long-term guarantee measures. For firms using internal models, this creates a benchmarking challenge: any divergence between the internal model SCR and the restated standard formula SCR requires explanation. Capital modelling teams must maintain the ability to run both calculations and reconcile the differences.

Climate risk integration into capital models is moving from aspiration to requirement. The PRA expects firms to incorporate climate scenarios into their Own Risk and Solvency Assessment (ORSA) and, for firms with internal models, to assess whether climate risk is adequately captured. For property catastrophe risk, this connects directly to catastrophe model assumptions about forward-looking hazard. For asset risk, it requires scenarios for transition risk and stranded assets. The challenge is that climate risk operates on timescales that extend well beyond the one-year Solvency II horizon.

How AI changes this

Faster scenario generation is the most immediate application. Traditional capital model runs are computationally expensive, often requiring hours or overnight batch processing for a full simulation. ML-based surrogate models, trained on the outputs of the full simulation, can approximate results in seconds for a defined range of input parameters. This enables real-time what-if analysis: an underwriter considering a large risk can see the marginal capital impact immediately rather than waiting for the next model run.

Automated sensitivity analysis identifies which assumptions and parameters have the greatest impact on the SCR. Traditional sensitivity testing involves running the model multiple times with each parameter varied individually, a time-consuming process that scales linearly with the number of parameters. AI-driven sensitivity analysis using techniques like Shapley values can identify the key drivers of capital consumption from a smaller number of model runs, directing actuarial attention to the assumptions that matter most.

Model validation acceleration uses AI to automate elements of the independent validation process. Comparing model outputs against historical experience, testing for internal consistency across risk modules, and checking that dependency structures produce plausible joint outcomes can be partially automated. This reduces the elapsed time for validation cycles and frees specialist resource for the judgemental aspects of validation that require human expertise.

Reserve risk modelling within the capital model benefits from the same ML-driven reserving insights discussed in claims reserving. Better individual claim reserve estimates feed into better reserve risk distributions, which feed into a more accurate SCR. The integration between reserving analytics and capital modelling is a significant source of value, but it requires the capital modelling team and the reserving team to work from consistent data and aligned assumptions.

What to know before you start

The PRA's approval process for internal model changes is the governing constraint. Any AI component that changes the SCR output is a major model change requiring pre-approval. Plan for the eighteen-month approval cycle when scoping AI enhancements to your internal model. Engage your PRA supervisor early, before building, to understand their expectations for AI components in internal models. No insurer has yet gained PRA approval for an ML-primary internal model component; you will be navigating new territory.

Surrogate models must be validated against the full model across the entire relevant parameter space, not just the central region. A surrogate that approximates the full model well for average scenarios but diverges in the tail, precisely where the SCR is calculated, is worse than useless. Validation of surrogate model accuracy in the tail requires large numbers of full model runs as benchmarks, which partially offsets the computational savings.

Capital modelling is a team sport that involves actuaries, risk managers, IT, and the board. AI enhancements that are developed by the data science team without deep involvement from the capital modelling actuaries will not pass the use test. The model must be understood by the people who use it in decision-making. Build cross-functional teams from the outset.

Start with sensitivity analysis and what-if tooling rather than changes to the core model. A surrogate model that enables faster scenario analysis for the board or the CRO adds immediate value without requiring a major model change application. This demonstrates the potential of AI in capital modelling while operating within the existing regulatory framework. Once the organisation and the regulator have confidence in AI-augmented capital analytics, the path to incorporating AI into the core model becomes more navigable. The resulting insights can also sharpen treaty pricing decisions by providing real-time views of marginal capital consumption.