Skip to main content Accessibility help
×
Home

ECONOMIC SCENARIO GENERATOR AND PARAMETER UNCERTAINTY: A BAYESIAN APPROACH

  • Jean-François Bégin (a1)

Abstract

In this article, we study parameter uncertainty and its actuarial implications in the context of economic scenario generators. To account for this additional source of uncertainty in a consistent manner, we cast Wilkie’s four-factor framework into a Bayesian model. The posterior distribution of the model parameters is estimated using Markov chain Monte Carlo methods and is used to perform Bayesian predictions on the future values of the inflation rate, the dividend yield, the dividend index return and the long-term interest rate. According to the US data, parameter uncertainty has a significant impact on the dispersion of the four economic variables of Wilkie’s framework. The impact of such parameter uncertainty is then assessed for a portfolio of annuities: the right tail of the loss distribution is significantly heavier when parameters are assumed random and when this uncertainty is estimated in a consistent manner. The risk measures on the loss variable computed with parameter uncertainty are at least 12% larger than their deterministic counterparts.

Copyright

Corresponding author

References

Hide All
Ahlgrim, K.C., D’Arcy, S.P. and Gorvett, R.W. (2004) Modeling of economic series coordinated with interest rate scenarios. Technical report, Casualty Actuarial Society and the Society of Actuaries.
Ahlgrim, K.C., D’Arcy, S.P., and Gorvett, R.W. (2008) A comparison of actuarial financial scenario generators. Variance 2, 111134.
Bernardo, J.M. and Smith, A.F. (2001) Bayesian Theory. New York, NY, USA: Wiley.
Bégin, J.-F. (2016) Deflation risk and implications for life insurers. Risks, 4, 46.
Cairns, A.J. (2000) A discussion of parameter and model uncertainty in insurance. Insurance: Mathematics and Economics, 27, 313330.
Cairns, A.J., Blake, D. and Dowd, K. (2006) A two-factor model for stochastic mortality with parameter uncertainty: theory and calibration. Journal of Risk and Insurance, 73, 687718.
Chan, T. (1998) Some applications of Lévy processes to stochastic investment models for actuarial use. ASTIN Bulletin, 28, 7793.
Chan, W.-S. (2002) Stochastic investment modelling: a multiple time-series approach. British Actuarial Journal, 8, 545591.
Chan, W.-S., Wong, A.C. and Tong, H. (2004) Some nonlinear threshold autoregressive time series models for actuarial use. North American Actuarial Journal, 8, 3761.
Fellingham, G.W., Kottas, A. and Hartman, B.M. (2015) Bayesian nonparametric predictive modeling of group health claims. Insurance: Mathematics and Economics, 60, 110.
Fisher, I. (1930) The Theory of Interest. New York, NY, USA: The Macmillan Co.
Gelman, A. and Rubin, D.B. (1992) Inference from iterative simulation using multiple sequences. Statistical Science, 7, 457472.
Geoghegan, T., Clarkson, R., Feldman, K., Green, S., Kitts, A., Lavecky, J., Ross, F., Smith, W. and Toutounchi, A. (1992) Report on the Wilkie stochastic investment model. Journal of the Institute of Actuaries, 119, 173228.
Gill, J. and Freeman, J.R. (2013) Dynamic elicited priors for updating covert networks. Network Science, 1, 6894.
Hartman, B.M. and Groendyke, C. (2013) Model selection and averaging in financial risk management. North American Actuarial Journal, 17, 216228.
Hartman, B.M. and Heaton, M.J. (2011) Accounting for regime and parameter uncertainty in regime-switching models. Insurance: Mathematics and Economics, 49, 429437.
Hartman, B.M., Richardson, R. and Bateman, R. (2017) Parameter uncertainty. Technical report, Casualty Actuarial Society, Canadian Institute of Actuaries, and Society of Actuaries Report.
Hastings, W.K. (1970) Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57, 97109.
Hayne, R.M. (1999) Modeling parameter uncertainty in cash flow projections. In CAS Forum, pp. 133151.
Heckman, P.E. and Meyers, G.G. (1983) The calculation of aggregate loss distributions from claim severity and claim count distributions. Proceedings of the Casualty Actuarial Society, 70, 2261.
Huber, P. (1997) A review of Wilkie’s stochastic asset model. British Actuarial Journal, 3, 181210.
Marceau, E. and Gaillardetz, P. (1999) On life insurance reserves in a stochastic mortality and interest rates environment. Insurance: Mathematics and Economics, 25, 261280.
Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H. and Teller, E. (1953) Equation of state calculations by fast computing machines. Journal of Chemical Physics, 21, 10871092.
Meyers, G. and Schenker, N. (1983) Parameter uncertainty in the collective risk model. PCAS LXX, p. 111.
Nolde, N. and Parker, G. (2014) Stochastic analysis of life insurance surplus. Insurance: Mathematics and Economics, 56, 113.
O’Hagan, A. (1998) Eliciting expert beliefs in substantial practical applications. Journal of the Royal Statistical Society: Series D (The Statistician), 47, 2135.
Pedersen, H., Campbell, M.P., Christiansen, S.L., Cox, S.H., Finn, D., Griffin, K., Hooker, N., Lightwood, M., Sonlin, S.M. and Suchar, C. (2016) Economic scenario generators: a practical guide. Technical report, Society of Actuaries.
Pflaumer, P. (2011) Methods for estimating selected life table parameters using the Gompertz distribution. In Proceedings of the Joint Statistical Meetings, Social Statistics Section, Miami Beach, pp. 733–747.
Redington, F.M. (1952) Review of the principles of life-office valuations. Journal of the Institute of Actuaries, 78, 286340.
Sahin, S., Cairns, A. and Kleinow, T. (2008) Revisiting the Wilkie investment model. In 18th International AFIR Colloquium, Rome, pp. 1–24.
Sherris, M., Tedesco, L. and Zehnwirth, B. (1997) Stochastic investment models: unit roots, cointegration, state space and GARCH models. In Actuarial Research Clearing House, Vol. 1, pp. 95144.
Upton, G. and Cook, I. (2014) A Dictionary of Statistics. New York: Oxford University Press.
Whitten, S. and Thomas, R.G. (1999) A non-linear stochastic asset model for actuarial use. British Actuarial Journal, 5, 919953.
Wilkie, A., Sahin, S., Cairns, A. and Kleinow, T. (2011) Yet more on a stochastic economic model, part 1: updating and refitting, 1995 to 2009. Annals of Actuarial Science, 5, 5399.
Wilkie, A.D. (1986) A stochastic investment model for actuarial use. Transactions of the Faculty of Actuaries, 39, 341403.
Wilkie, A.D. (1995) More on a stochastic asset model for actuarial use. British Actuarial Journal, 1, 777964.
Wilkie, A.D. and Sahin, S. (2016) Yet more on a stochastic economic model: part 2: initial conditions, select periods and neutralising parameters. Annals of Actuarial Science, 10, 151.
Wilkie, A.D. and Sahin, S. (2017 a) Yet more on a stochastic economic model: part 3A: stochastic Interpolation: Brownian and Ornstein–Uhlenbeck (OU) Bridges. Annals of Actuarial Science, 11, 7499.
Wilkie, A.D. and Sahin, S. (2017 b) Yet more on a stochastic economic model: part 3B: stochastic bridging for retail prices and wages. Annals of Actuarial Science, 11, 100127.
Wilkie, A.D. and Sahin, S. (2017 c) Yet more on a stochastic economic model: part 3C: stochastic bridging for share yields and dividends and interest rates. Annals of Actuarial Science, 11, 128163.
Wilkie, A.D. and Sahin, S. (2018) Yet more on a stochastic economic model: part 4: a model for share earnings, dividends, and prices. Annals of Actuarial Science, 12, 67105.
Zhang, L., Mykland, P.A. and At-Sahalia, Y. (2005) A tale of two time scales. Journal of the American Statistical Association, 100, 13941411.
Zhang, S., Hardy, M. and Saunders, D. (2018) Updating Wilkie’s economic scenario generator for U.S. applications. North American Actuarial Journal, 22, 600622.

Keywords

Type Description Title
PDF
Supplementary materials

Bégin et al. supplementary material
Bégin et al. supplementary material 1

 PDF (536 KB)
536 KB

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed