Risk management of variable annuity portfolios using machine learning techniques

Abstract

Variable annuities (VAs) are increasingly becoming popular insurance products in many developed countries which provide guaranteed forms of income depending on the performance of the equity market. Insurance companies often hold large VA portfolios and the associate valuation of such portfolios is a very time-consuming task. There have been several studies focusing on inventing techniques aimed at reducing the computational time including the selection of representative VA contracts and the use of a metamodel to estimate the values of all contracts in the portfolio. In this thesis, LASSO regression is used to select a set of representative scenarios after the representative contracts are chosen, which in turn allows for the set of representative contracts to expand without significant increase in computational load. The proposed approach leads to a remarkable improvement in the computational efficiency and accuracy of the metamodel. Stochastic reserving and calculation of capital requirement require VA providers to calculate risk measures such as Value at Risk and Conditional Tail Expectation. An emulation framework is proposed to calculate these risk measures by building a neural network to model the net liability of a VA contract at some given scenario. The surrogate model is faster at estimating net liability than the exact calculation. Efficiency is improved thanks to faster computing of net liability for any contract at any scenario in the Monte Carlo simulation. This approach can also be used to select scenarios where the estimated portfolio liabilities are in the top quantile. The true liabilities of the portfolio at these top-quantile scenarios can be computed which can then be used to compute the risk measures. This results in a reduction in computational time because the Monte Carlo method is performed on only a fraction of the original scenarios. As an equity-linked insurance products, VA is exposed to significant market risks due to the underlying assets in the mutual funds that its contributions are invested in. To hedge against these market risks, insurers need to construct a hedging portfolio consisting of the underlying assets whose hedge positions can be determined by the Greeks of the portfolio such as the partial dollar Deltas. For a large portfolio, the calculation of the Greeks using Monte Carlo simulation is very slow, so a metamodeling approach can be used to estimate the Greeks. Assuming that the mutual funds of the VA insurers is a mixture of major market indices, there is likely a dependence between the partial dollar Deltas of the portfolio on the market indices. This dependent relationship can be incorporated into the model using multi-output regression approaches and the resulting improvement in the effectiveness of the metamodel or the lack thereof will be studied in the thesis