Within a Monte Carlo simulation framework, variance reduction is a vital part of the valuation of insurance liabilities. The complex nature of insurance products and their exposure towards a variety of risk factors—which usually are stochastically simulated—typically leads to a large number of scenarios, required to derive estimates for the expected value of these liabilities. The reliability of these estimates is measured by a confidence interval, normally in terms of the standard deviation of the sampled values. Well-known square root convergence, however, implies that reducing the confidence interval of the estimates by increasing the number of simulations is not very efficient. The run-times involved in the valuation of the insurance liabilities are a crucial factor for the steering and management of insurance companies.
Therefore, insurers turn towards variance reduction techniques that allow for scaling down the remaining variance without increasing the overall simulation budget. While the implementation of these methods typically requires a change of the overall simulation framework, we present in this document a new control variate approach that works within the existing simulation framework. It achieves a reduction of variance by combining the leakage of the simulation model with the liability value under consideration in a smart way. This report demonstrates that model leakage can be efficiently used as a control variate to reduce the variance of economic valuations of insurance liabilities.
This paper has been co-authored with Andreas Meister, Marcel Ambrus and Urs Burri from Baloise, Switzerland.