Solvency II proxy modelling via Least Squares Monte Carlo

For European life insurers that have decided to implement Solvency II on an internal model basis, it is necessary to consider two stochastic dimensions: a so called “outer” real-world one to capture the probability distribution of different outcomes for the economic balance sheet over a one year time horizon and an “inner” risk neutral one in order to value assets and liabilities along each of these real world paths. Such a calculation would require a nested stochastic approach, which for many companies is very difficult or simply impractical due to the number of runs necessary.

This has led companies to look for proxy modelling techniques which can estimate the full approach in more acceptable run times. Methods used to date include replicating portfolios and curve fitting, but neither of these techniques is straightforward and when there are complex interactions between assets and liabilities, there may be difficulty getting an adequate level of fit. Recently a lot of attention has focused on another technique, Least Square Monte Carlo (LSMC). In the LSMC method we do not use thousands, but just a small number (e.g., 10) of inner valuation scenarios for each outer one. This gives a very inaccurate valuation, but by carrying out a regression we can arrive at a very good estimate of the precise calculation we would get from a full nested stochastic approach.

Via LSMC, we can obtain very accurate results at a fast run time. The accuracy of LSMC results can be verified in a practically robust and statistically sound way. The LSMC method requires much less manual intervention than some of the alternatives and can give valuable economic insights about the interplay of different risk drivers.

In this paper we explain the process used to carry out the LSMC calculation and give a realistic example of its application to a hypothetical German life insurer.