Hostname: page-component-76fb5796d-25wd4 Total loading time: 0 Render date: 2024-04-26T14:27:49.409Z Has data issue: false hasContentIssue false

Fast Sensitivity Computations for Monte Carlo Valuation of Pension Funds

Published online by Cambridge University Press:  09 August 2013

Mark Joshi
Affiliation:
University of Melbourne, E-Mail: mark@markjoshi.com
David Pitt
Affiliation:
Department of Actuarial Studies, Macquarie University, NSW 2109, Australia, E-mail: david.pitt@mq.edu.au

Abstract

Sensitivity analysis, or so-called ‘stress-testing’, has long been part of the actuarial contribution to pricing, reserving and management of capital levels in both life and non-life assurance. Recent developments in the area of derivatives pricing have seen the application of adjoint methods to the calculation of option price sensitivities including the well-known ‘Greeks’ or partial derivatives of option prices with respect to model parameters. These methods have been the foundation for efficient and simple calculations of a vast number of sensitivities to model parameters in financial mathematics. This methodology has yet to be applied to actuarial problems in insurance or in pensions. In this paper we consider a model for a defined benefit pension scheme and use adjoint methods to illustrate the sensitivity of fund valuation results to key inputs such as mortality rates, interest rates and levels of salary rate inflation. The method of adjoints is illustrated in the paper and numerical results are presented. Efficient calculation of the sensitivity of key valuation results to model inputs is useful information for practising actuaries as it provides guidance as to the relative ultimate importance of various judgments made in the formation of a liability valuation basis.

Type
Research Article
Copyright
Copyright © International Actuarial Association 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Booth, P., Chadburn, R., Cooper, D., Haberman, S. and James, D. (1999) Modern Actuarial Theory and Practice. Chapman and Hall/CRC, London.Google Scholar
Brender, A. (1988) Testing the solvency of life insurers. Proceedings of the 2nd International Conference on Insurance Solvency.Google Scholar
Chan, J.-H. and Joshi, M. (2009) Fast Monte-Carlo Greeks for Financial Products With Discontinuous Pay-Offs. http://ssrn.com/abstract=15003 CrossRefGoogle Scholar
Glasserman, P. and Giles, M. (2006) Smoking adjoints: fast Monte Carlo Greeks. Risk, January 2006, 9296.Google Scholar
Glasserman, P. (2004) Monte Carlo Methods in Financing Engineering. Springer-Verlag, Berlin-Heidelberg-New York.Google Scholar
Griewank, A. (2000) Evaluating derivatives: principles and techniques of algorithmic differentiation. Society for Industrial and Applied Mathematics.Google Scholar
Joshi, M. and Kwon, O.K. (2010) Monte Carlo Market Greeks in the Displaced Diffusion LIBOR Market Model. http://ssrn.com/abstract=1535058 CrossRefGoogle Scholar
Lee, R.D. and Carter, L. (1992) Modeling and Forecasting the Time Series of US Mortality. Journal of the American Statistical Association 87, 659671.Google Scholar
Neill, A. (1977) Life Contingencies, Butterworth-Heinemann Ltd. Google Scholar