European insurance companies are seeking enhanced analytical tools to help manage the modelling requirements under Solvency II. Milliman’s Tigran Kalberer discusses using replicating portfolio techniques, least-squares Monte Carlo approaches, and curve fitting for estimating the risk capital of a life insurer in this InsuranceERM article (subscription required).
Here is an excerpt:
In recent years, a number of different proxy approaches have been introduced to make solvency capital requirement (SCR) calculations more manageable. Proxy approaches for SCR calculation purposes are generally based on finding (simpler) functions which approximate a value function and minimise the sum of the squared differences to the given value function over a set of so-called calibration scenarios, potentially under certain constraints. The best-known approaches applied in the insurance industry are:
• Replicating portfolio techniques (RPT)
• Least-squares Monte Carlo (LSMC)
• Curve fitting
The common idea underlying all these approaches is that the valuation of the liabilities is not performed directly but an approximation for the values is used (see figure 2). Although the calibration techniques underlying the proxy approaches are different, the application is similar in the sense that they assume that on the set of calibration scenarios the approximating function is a linear combination of “basis functions.” While RPT and LSMC essentially ask to solve an optimisation problem and thus find a good fit of basis functions, curve fitting looks to determine a basis function which fits selected sensitivities.