Valuation of Large Variable Annuity Portfolios Under Nested Simulations: A Functional Data Approach

Gan, G. and Lin, X.S. (2015). Valuation of large variable annuity portfolios under nested simulation: a functional data approach, Insurance: Mathematics and Economics, 62, 138-150.

13 Pages Posted: 22 Nov 2013 Last revised: 26 Dec 2015

See all articles by Guojun Gan

Guojun Gan

Manulife Asset Management

X. Sheldon Lin

Department of Statistical Sciences, University of Toronto

Date Written: November 21, 2013

Abstract

Variable annuities are equity-linked annuity products that have rapidly grown in popularity around the world in recent years. Research up to date on variable annuity largely focuses on the valuation of guarantees embedded in a single variable annuity contract. However, methods developed for individual VA contracts based on option pricing theory cannot be extended to large variable annuity portfolios. Insurance companies currently use nested simulations to value guarantees for variable annuity portfolios but efficient valuation under nested simulations for a very large variable annuity portfolio has been a real challenge. The computation in nested simulations are highly intensive and often prohibitive. In this paper, we propose a novel method that combines a clustering technique with a functional data analysis technique to address this issue. We create a highly non-homogeneous synthetic variable annuity portfolio of 100,000 contracts and use it to estimate the dollar Deltas of the portfolio at each time step of outer loop scenarios under the nested simulation framework over a period of 30 years. Our test results show that the proposed method performs well in terms of accuracy and efficiency.

Keywords: Variable annuity, Monte Carlo simulation, Nested simulation, Stochastic-on-stochastic, Portfolio valuation, Clustering, Functional data analysis

JEL Classification: G12, G13

Suggested Citation

Gan, Guojun and Lin, Xiaodong Sheldon, Valuation of Large Variable Annuity Portfolios Under Nested Simulations: A Functional Data Approach (November 21, 2013). Gan, G. and Lin, X.S. (2015). Valuation of large variable annuity portfolios under nested simulation: a functional data approach, Insurance: Mathematics and Economics, 62, 138-150., Available at SSRN: https://ssrn.com/abstract=2358231 or http://dx.doi.org/10.2139/ssrn.2358231

Guojun Gan (Contact Author)

Manulife Asset Management ( email )

200 Bloor Street East
NT-5
Toronto, Ontario M4W1E5
Canada

Xiaodong Sheldon Lin

Department of Statistical Sciences, University of Toronto ( email )

Department of Statistical Sciences
100 St George Street
Toronto, Ontario M5S 3G3
Canada

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