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Nested Simulations in Life Insurance

Daniela Bergmann, 2011, ISBN: 978-3-942493-04-8

1. Preis SCOR-Wettbewerb 2011

In recent years, market-consistent valuation has gained an increasing importance for life insurance companies. However, due to the complex structure of life insurance contracts containing embedded options and guarantees, the market-consistent valuation of an insurer’s liabilities can generally not be done in closed form. Therefore, life insurance companies often rely on Monte Carlo simulations.

But in many situations, the proper valuation of insurance liabilities via Monte Carlo simulations leads to so-called „nested simulations“ where in every sample path of one Monte Carlo simulation another Monte Carlo simulation is required at least at one point in time. Due to the resulting nested structure, the corresponding calculations are usually extremely time-consuming. In fact, in many practical applications, nested simulations may even not be feasible due to constraints in computational resources. As a consequence, many life insurance companies rely on second-best approximations, which are often not able to accurately reflect the insurer’s liabilities and/or risk exposure and may thus lead to deficient outcomes. Therefore, there is a need for theoretically motivated techniques that are computationally feasible and model the insurer’s liabilities and risks more appropriately.

In this monograph, we analyze two different simulation problems relevant to life insurance companies where a simple Monte Carlo approach leads to nested simulations: the valuation of life insurance contracts containing early-exercise features and the calculation of the Solvency Capital Requirement (SCR) based on an internal model in the framework of Solvency II. We discuss different methodologies and show how sophisticated techniques may be used to improve on the simple nested simulations approach. In particular, we show that significant efficiency gains can be achieved.

 

Terms: Nested simulations, life insurance, surrender options, Solvency II, Solvency Capital Requirement

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