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Metamodels, which simplify the simulation models used in the valuation of large variable annuity portfolios, have recently increased in popularity. The ordinary kriging and the GB2 regression models are examples of metamodels used to predict fair market values of variable annuity guarantees. It is well known that the distribution of fair market values is highly skewed. Ordinary kriging does not fit well skewed data but it depends only on a few parameters that can be estimated straightforwardly. GB2 regression can handle skewed data but its parameter estimation can be quite challenging. In this paper, we explore the rank order kriging method, which can handle highly skewed data and depends only on a single parameter, for the valuation of large variable annuity portfolios. Our numerical results demonstrate that the rank order kriging method performs remarkably well in terms of fitting the skewed distribution and producing accurate estimates of fair market values at the portfolio level.
This book is devoted to the mathematical methods of metamodeling that can be used to speed up the valuation of large portfolios of variable annuities. It is suitable for advanced undergraduate students, graduate students, and practitioners. It is the goal of this book to describe the computational problems and present the metamodeling approaches in a way that can be accessible to advanced undergraduate students and practitioners. To that end, the book will not only describe the theory of these mathematical approaches, but also present the implementations.
Metamodeling techniques have recently been proposed to address the computational issues related to the valuation of large portfolios of variable annuity contracts. However, it is extremely difficult, if not impossible, for researchers to obtain real datasets from insurance companies in order to test their metamodeling techniques on such real datasets and publish the results in academic journals. Even if a researcher can obtain real datasets from insurance companies, it is difficult for the re- searcher to share the datasets with the public at large. To facilitate the development and dissemination of research related to the efficient valuation of large variable annuity portfolios, this paper creates a large synthetic portfolio of variable annuity contracts based on the properties of real portfolios of variable annuities and implements a Monte Carlo simulation engine for valuing the synthetic portfolio. In addition, this paper develops benchmark datasets of fair market values and Greeks, which are important quantities for managing the financial risks associated with variable annuities. The resulting datasets provide researchers with a common basis for testing and comparing the performance of various metamodeling techniques.
A computationally appealing methodology for the valuation of large variable annuities portfolios is a metamodelling framework that evaluates a small set of representative contracts, fits a predictive model based on these computed values, and then extrapolates the model to estimate the values of the remaining contracts. This paper proposes a new two-phase procedure for selecting representative contracts. The representatives from the first phase are determined using contract attributes as in existing metamodelling approaches, but those in the second phase are chosen by utilizing the information contained in the values of the representatives from the first phase. Two numerical studies confirm that our two-phase selection procedure improvesupon conventional approaches from the existing literature.
The valuation of variable annuity (VA) portfolios presents major challenges for life insurers. Recent studies propose approximation methods based on selecting a few representative guarantees. In contrast, I present a "bottom-up" valuation approach using recursive dynamic programming (RDP). An in-depth numerical analysis shows that the RDP estimation is able to value a large VA portfolio with a high degree of accuracy and within a few seconds--even under stochastic interest rates and volatility--since the heavy computational burden can be fully front-loaded (in a one-time effort at the guarantee's pricing stage). The RDP approach outperforms competing methods in both speed and accuracy and is thus ideally suited for various VA-related applications, including the computation of GAAP reserves, statutory reserves and capital requirements, as well as to determine the insurer's hedging position. Moreover, RDP can naturally incorporate optimal policyholder behavior into the insurer's valuation.
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 associated valuation of such portfolios for hedging purposes 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 addition to the selection of representative contracts, this paper proposes using LASSO regression to select a set of representative scenarios, 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.
The nested-simulation is commonly used for calculating the predictive distribution of the total variable annuity (VA) liabilities of large VA portfolios. Due to the large numbers of policies, inner-loops and outer-loops, running the nested-simulation for a large VA portfolio (100K+) is extremely time consuming and often prohibitive. In this paper, the use of surrogate models is incorporated into the nested-simulation algorithm so that the relationship between the inputs and the outputs of a simulation model is approximated by various statistical models. As a result, the nested-simulation algorithm can be run with much smaller numbers of different inputs. Specifically, a spline regression model is used to reduce the number of outer-loops and a model-assisted finite population estimation framework is adapted to reduce the number of policies in use for the nested-simulation. From simulation studies, our proposed algorithm is able to accurately approximate the predictive distribution of the total VA liability at a significantly reduced running time.
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