Scenario Selection With Lasso Regression For The Valuation Of Variable Annuity Portfolios PDF Download

Variable annuities (VAs) are equity-linked annuities with embedded investment guarantees. Their long-term security and tax deferred features have made them one of the major insurance products in the world. Nowadays, many insurance companies are managing large VA portfolios that contain hundreds of thousands policies. Since most of the VA contributions are invested in the equity market, the insurance companies are exposed to significant market risks and risk managing the VA liabilities has become the central task. In practice, the stochastic-on-stochastic nested simulation is commonly used for VA portfolio valuation and risk management. The path-dependency of the embedded guarantees and the non-homogeneity of the VA policies make the nested simulation algorithm extremely complex and time-consuming to run. As a result, timely managing the portfolio risks becomes a major challenge to the insurance companies. The complexity of the nested simulation algorithm depends directly on three components: the number of policies, the number of outer-loop simulation, and the number of inner-loop simulation. In this thesis, we incorporate the idea of surrogate modelling to the nested simulation algorithm such that all of the input dimensions are reduced. The surrogate models act as proxies to approximate the input/output relationships. Since only a few input points are needed in order to identify the surrogate models, the simulation time could be shortened significantly. The key feature of the proposed algorithm is that the methodologies for selecting the inputs are theoretically justifiable from the statistical properties of the surrogate models. As a result, a robust performance can be ensured for the proposed algorithm in different context. Specifically, we introduce a model-assisted estimation framework with balanced sampling to reduce the number of policies, and a spline regression framework with scenario clustering to reduce the number of outer-/inner-loops. The proposed algorithm is applied to perform various valuations for large synthetic VA portfolios such as calculating the predictive liability distribution, the portfolio Greeks, and the regulatory capital requirement with dynamic hedging. The efficiency and the robustness of the algorithm are demonstrated through numerical studies on a number of uniform/non-uniform large synthetic VA portfolios and economics models.