A regime-switching model of long-term stock returns. (English) Zbl 1083.62530

Summary: I first define the regime-switching lognormal model. Monthly data from the Standard and Poors 500 and the Toronto Stock Exchange 300 indices are used to fit the model parameters, using maximum likelihood estimation. The fit of the regime-switching model to the data is compared with other common econometric models, including the generalized autoregressive conditionally heteroskedastic model. The distribution function of the regime-switching model is derived. Prices of European options using the regime-switching model are derived and implied volatilities explored. Finally, an example of the application of the model to maturity guarantees under equity-linked insurance is presented. Equations for quantile and conditional tail expectation (Tail-VaR) risk measures are derived, and a numerical example compares the regime-switching lognormal model results with those using the more traditional lognormal stock return model.


62P05 Applications of statistics to actuarial sciences and financial mathematics
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
91G70 Statistical methods; risk measures
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[1] Akaike H., IEEE Trans Aut Control 19 pp 716– (1974) · Zbl 0314.62039
[2] Artzner P., Coherent Measures of Risk 9 pp 203– (1999)
[3] Bollen N. P. B., Journal of Derivatives 6 pp 38– (1998)
[4] Bollerslev T., Journal of Econometrics 31 pp 307– (1986) · Zbl 0616.62119
[5] Engle R. F., Econometrica 50 pp 987– (1982) · Zbl 0491.62099
[6] Hamilton J. D., Econometrica 57 pp 357– (1989) · Zbl 0685.62092
[7] Hamilton J. D., Time Series Analysis (1994) · Zbl 0831.62061
[8] Hamilton J. D., Journal of Econometrics 64 pp 307– (1994) · Zbl 0825.62950
[9] Hardy M. R., Stock Return Models for Segregated Fund Guarantees (1999)
[10] Harris G. R., Proceedings of the 7th International AFIR Colloquium 1 pp 421– (1997)
[11] Klugman S., Ross Models: From Data to Decisions (1998)
[12] Schwartz G., Annals of Statistics 6 pp 461– (1978) · Zbl 0379.62005
[13] Task Force on Segregated Funds, Report of the Task Force on Segregated Fund Investment Guarantees (2000)
[14] Wilkie A. D., British Actuarial Journal 1 pp 777– (1995)
[15] Wirch J. L., Insurance: Mathematics and Economics 25 pp 337– (1999) · Zbl 0951.91032
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