Towards simpler numerical methods for the management of assets and liabilities

Insurance companies deal with risk on a day-to-day basis. One of most critical they are exposed to is the eventuality of a mismatch between assets and liabilities, or in other words, between what they own and they owe. In the European Union, to reduce this risk, insurance and reinsurance companies are required at all times to hold a certain amount of funds called the Solvency Capital Requirement (SCR). This capital is calculated on a yearly basis, and is intended to ensure that claims can be met when they are due. But the determination of the required capital is really complex. In a Joint Initiative with AXA, prof. Aurélien Alfonsi, of the Ecole Nationale des Ponts et Chaussées, in Paris, aims to develop numerical methods that reduces computation time for the calculation of SCRs. The overarching objective is to enable the optimization of overall models for the management of assets and liabilities (ALM) in insurance companies.

Indeed, insurance companies must rethink their long-term investment strategy periodically. To do so, they increasingly rely on large-scale, sophisticated asset-liability models that carefully consider current and long-term potential earnings, balance them with the need to maintain adequate liquidity and attempt to take into account all significant quantifiable risks. «This type of study requires many simulations and results in significant computation time. Thus, a real challenge is to propose a synthetic model that takes into account the main sources of risk, with a quite minimal parametrization, explains prof. Aurélien Alfonsi. And in order to keep run times manageable, some approximations have to be made, especially on the Solvency Capital Requirement.» This is where this expert in stochastic calculus and finance comes in: developing new numerical methods to simplify SCR calculation. « The challenge is to do so without extrapolating, which is what insurance companies are doing at the moment, he specifies. This leads to inaccuracies. Instead, the idea is really to capture the essential, and it doesn’t necessarily involve going into too many details. The goal is not to get an ultra-realistic model, but instead to propose the simplest model possible that does not discard the main risks in ALM », he summarizes.

Reducing calculation time, without extrapolating

To do so, the project aims to develop new dedicated algorithms for the ALM, called Monte Carlo simulations. This type of numerical method is used to model the probability of different outcomes in a process that cannot easily be predicted due to the intervention of random variables. It is a technique used to understand the impact of risk and uncertainty in prediction and forecasting models. More specifically, the research objective is first to set up a relevant and tractable model for the main asset classes (equity, interest rates bonds, real estate... ) and for the main liabilities. «To achieve that, we’ve spent a lot of time trying to understanding in details how ALM works. We needed this to model the whole process correctly », prof. Alfonsi specifies. This preliminary approach is meant to open the way for the key step of the project: the development of the nested numerical methods for the calculation of the SCR. Once this is done, the AXA teams will consider the problem of optimizing the strategic asset allocation by using this new precise evaluation of the SCR. « AXA’s involvement in the project is paramount, the researcher insists. It would have been meaningless to tackle such a goal without the support and the feedback of practitioners. AXA will bring to the project its expertise in the field of the Asset Liability Management, from a technical and methodological point of view but also from the regulatory side. In particular, they will help us to assess the performance of the method with respect to the existing ones and to the standard formula given for the SCR by the European Commission ».

The rationale behind this Joint Initiative is simple: better numerical models for SCR will improve long-term ALM studies, and thus increase the profitability of the company’s strategies. The aim of the project is in alignment with the needs of insurance companies: obtain a “good” trade-off between realism, computation time and tractability. The output will not only benefit AXA France, but will also be presented in different international conferences.