Economic Scenario Generators: a risk management tool for insurance

We present a risk management tool, named Economic Scenario Generator (ESG), used by insurance companies for simulating the global state of one or several economies described by key financial risk drivers. This tool is of particular use within the Solvency II framework, since insurance companies are required to value their balance-sheet from a market-consistent viewpoint. However, there is no observable price of insurance contracts hence the necessity of relying on ESGs to perform Monte Carlo simulations useful for valuation. As such, the calibration of Risk-Neutral models underlying this valuation is of particular interest as there is a strong requirement to match observable market prices. Furthermore, for a variety of applications, the insurance company has to value its balance-sheet over a set of different economic conditions, leading to the need of intensive re-calibrations of such models. In this paper, we first provide an overview of the key requirements from Solvency II and their practical implications for insurance valuation. We then describe the different use cases of ESGs. A particular attention is paid to Risk-Neutral interest rates models, specifically the Libor Market Model with a stochastic volatility. We discuss the complexity of its calibration and describe fast calibration methods based on approximations and expansions of the probability density function. Comparisons with more common method highlight the reduction in calibration time.