A Spatial Interpolation Framework for Efficient Valuation of Large Portfolios of Variable Annuities

Seyed Amir Hejazi; Kenneth R. Jackson; Guojun Gan; Seyed Amir Hejazi; Kenneth R. Jackson; Guojun Gan

doi:10.3934/QFE.2017.2.125

Quantitative Finance and Economics

2017, Volume 1, Issue 2: 125-144. doi: 10.3934/QFE.2017.2.125

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A Spatial Interpolation Framework for Efficient Valuation of Large Portfolios of Variable Annuities

1.
Department of Computer Science, University of Toronto, Toronto, ON, M5S 3G4, Canada
2.
Department of Mathematics, University of Connecticut, Storrs, Connecticut, 06269-3009, USA

Received: 29 April 2017 Accepted: 13 June 2017 Published: 14 July 2017

Abstract
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Variable Annuity (VA) products expose insurance companies to considerable risk because of the guarantees they provide to buyers of these products. Managing and hedging these risks require insurers to find the values of key risk metrics for a large portfolio of VA products. In practice, many companies rely on nested Monte Carlo (MC) simulations to find key risk metrics. MC simulations are computationally demanding, forcing insurance companies to invest hundreds of thousands of dollars in computational infrastructure per year. Moreover, existing academic methodologies are focused on fair valuation of a single VA contract, exploiting ideas in option theory and regression. In most cases, the computational complexity of these methods surpasses the computational requirements of MC simulations. Therefore, academic methodologies cannot scale well to large portfolios of VA contracts. In this paper, we present a framework for valuing such portfolios based on spatial interpolation. We provide a comprehensive study of this framework and compare existing interpolation schemes. Our numerical results show superior performance, in terms of both computational effciency and accuracy, for these methods compared to nested MC simulations. We also present insights into the challenge of finding an effective interpolation scheme in this framework, and suggest guidelines that help us build a fully automated scheme that is effcient and accurate.
- variable annuity,
- spatial interpolation,
- Kriging,
- inverse distance weighting,
- radial basis function,
- portfolio valuation
Citation: Seyed Amir Hejazi, Kenneth R. Jackson, Guojun Gan. A Spatial Interpolation Framework for Efficient Valuation of Large Portfolios of Variable Annuities[J]. Quantitative Finance and Economics, 2017, 1(2): 125-144. doi: 10.3934/QFE.2017.2.125

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Abstract

Variable Annuity (VA) products expose insurance companies to considerable risk because of the guarantees they provide to buyers of these products. Managing and hedging these risks require insurers to find the values of key risk metrics for a large portfolio of VA products. In practice, many companies rely on nested Monte Carlo (MC) simulations to find key risk metrics. MC simulations are computationally demanding, forcing insurance companies to invest hundreds of thousands of dollars in computational infrastructure per year. Moreover, existing academic methodologies are focused on fair valuation of a single VA contract, exploiting ideas in option theory and regression. In most cases, the computational complexity of these methods surpasses the computational requirements of MC simulations. Therefore, academic methodologies cannot scale well to large portfolios of VA contracts. In this paper, we present a framework for valuing such portfolios based on spatial interpolation. We provide a comprehensive study of this framework and compare existing interpolation schemes. Our numerical results show superior performance, in terms of both computational effciency and accuracy, for these methods compared to nested MC simulations. We also present insights into the challenge of finding an effective interpolation scheme in this framework, and suggest guidelines that help us build a fully automated scheme that is effcient and accurate.

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