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More on a Stochastic Asset Model for Actuarial Use

Published online by Cambridge University Press:  10 June 2011

A.D. Wilkie
A.D. Wilkie
Affiliation:
Dennington, Ridgeway, Horsell, Woking, Surrey, GU21 4QR, U.K. Tel: +44 (0)1483 725984; Fax: +44 (0)1483 725984; E-mail: [email protected]
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Abstract

In this paper the ‘Wilkie investment model’ is discussed, updated and extended. The original model covered price inflation, share dividends, share dividend yields (and hence share prices) and long-term interest rates, and was based on data for the United Kingdom from 1919 to 1982, taken at annual intervals. The additional aspects now covered include: the extension of the data period to 1994 (with omission of the period from 1919 to 1923); the inclusion of models for a wages (earnings) index, short-term interest rates, property rentals and yields (and hence property prices) and yields on index-linked stock; consideration of data for observations more frequently than yearly, in particular monthly data; extension of the U.K. model to certain other countries; introduction of a model for currency exchange rates; extension of certain aspects of the model to a larger number of other countries; and consideration of more elaborate forms of time-series modelling, in particular cointegrated models and ARCH models.

Keywords

Stochastic Asset ModelsWilkie ModelTime-Series ModelsPrice InflationWagesShare Dividend Yields, Dividends and PricesLong-Term and Short-Term Interest RatesProperty RentalsYields and PricesIndex-Linked YieldsExchange RatesCointegrated Time SeriesARCH Models
Type
Sessional meetings: papers and abstracts of discussions
Information
British Actuarial Journal , Volume 1 , Issue 5 , 01 December 1995 , pp. 777 - 964
Copyright
Copyright © Institute and Faculty of Actuaries 1995

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References

REFERENCES

Baillie, R.T. & Selover, D.D. (1987). Cointegration and models of exchange rate determination. International Journal of Forecasting, 3, 43–51.CrossRefGoogle Scholar
Banker's Almanac (1988). Reid Information Services, East Grinstead.Google Scholar
Bollerslev, T., Chou, R.Y. & Kroner, K.F. (1992). ARCH modelling in finance: a review of the theory and empirical evidence. Journal of Econometrics, 52, 5–59.CrossRefGoogle Scholar
Bonsdorff, H. (1991). A model for investment returns: asymptotic behaviour. Transactions of the 2nd AFIR International Colloquium, Brighton, 4, 27–37.Google Scholar
Bonsdorff, H., Pentikainen, T., Pesonen, M., Pukkila, T., Ranne, A., Rantala, J., Ruohonen, M. & Sarvamaa, S. (FIM GROUP) (1994). On the asset models as part of all company insurance analysis. Transactions of the 4th International AFIR Colloquium, Orlando, 3, 1471–1501.Google Scholar
Box, G.E.P. & Jenkins, G.M. (1976). Time series analysis, forecasting and control. Holden-Day, San Francisco.Google Scholar
Brockwell, P.J. & Davis, R.A. (1991). Time series: theory and methods. Second edition, Springer-Verlag, New York.CrossRefGoogle Scholar
Carter, J. (1991). The derivation and application of an Australian stochastic investment model. Transactions of the Institute of Actuaries of Australia. 1991, 1, 315–428.Google Scholar
Central Statistical Office (1972). Financial statistics: notes and definitions. H.M.S.O., London.Google Scholar
Central Statistical Office (1972–1994). Financial statistics, monthly. H.M.S.O., London.Google Scholar
Chatfield, C. (1980). The analysis of lime series: an introduction. Second edition, Chapman and Hall, London.CrossRefGoogle Scholar
Clarkson, R.S. (1991). A non-linear stochastic model for inflation. Transactions of the 2nd AFIR International Colloquium, Brighton, 3, 233–253.Google Scholar
Corbae, D. & Ouliaris, S. (1988). Cointegration and tests of purchasing power parity. Review of Economics and Statistics, 70, 508–511.CrossRefGoogle Scholar
Cox, D.R. & Miller, H.D. (1965). The theory of stochastic processes. Methuen, London.Google Scholar
Craighead, S. (1994). Chaotic analysis on U.S. Treasury interest rates. Transactions of the 4th AFIR International Colloquium, Orlando, 2, 497–536.Google Scholar
Cryer, J.D. (1986). Time series analysis. Duxbury Press, Boston.Google Scholar
Daykin, C.D. & Hey, G.B. (1990). Managing uncertainty in a general insurance company. J.I.A. 117, 173–277.Google Scholar
Daykin, C.D. & Hey, G.B. (1991). A stochastic cash-flow model of a general insurance company. Transactions of the 2nd AFIR International Colloquium, Brighton, 4, 113–137.Google Scholar
Daykin, C.D., Pentikainen, T. & Pesonen, M. (1994). Practical risk theory for actuaries. Chapman & Hall, London.Google Scholar
Deaves, R. (1993). Modelling and predicting Canadian inflation and interest rates. Canadian Institute of Actuaries.Google Scholar
Department of Employment (1971). British labour statistics: historical abstract 1886–1968. H.M.S.O., London.Google Scholar
Department of Employment (1986). Retail price indices, 1914–1985. H.M.S.O., London.Google Scholar
Dickey, D.A. & Fuller, W.A. (1979). Distributions of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association, 75, 427–431.Google Scholar
Dickey, D.A. & Fuller, W.A. (1981). Likelihood ratio statistics for autoregressive time series with a unit root. Econometrica, 49, 1057–1072.CrossRefGoogle Scholar
Douglas, C.M. (1930). The statistical groundwork of investment policy. T.F.A. 12, 173–228.Google Scholar
Duffie, D. (1992). Dynamic pricing theory. Princeton University Press, Princeton, N.J.Google Scholar
Enders, W. (1988). ARIMA and cointegration tests of PPP under fixed and flexible exchange rate regimes. Review of Economics and Statistics, 70, 504–508.CrossRefGoogle Scholar
Engle, R.F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50, 987–1007.CrossRefGoogle Scholar
Engle, R.F. & Granger, C.W.J., Editors (1991). Long-run economic relationships; readings in cointegration. Oxford University Press.CrossRefGoogle Scholar
Everitt, B.S. & Hand, D.J. (1981). Finite mixture distributions. Chapman and Hall, London.CrossRefGoogle Scholar
Fama, E.F. & French, R.K. (1988). Dividend yields and expected stock returns. Journal of Financial Economics, 22, 3–25.CrossRefGoogle Scholar
Fisher, I. (1907). The rate of interest. The Macmillan Company, New York.Google Scholar
Fisher, I. (1930). The theory of interest. The Macmillan Company, New York. Reprinted (Kelley), 1955.Google Scholar
Geoghegan, T.J., Clarkson, R.S., Feldman, K.S., Green, S.J., Kitts, A., Lavecky, J.P., Ross, F.J.M., Smith, W.J. & Toutounchi, A. (1992). Report on the Wilkie stochastic investment model. J.I.A. 119, 173–228.Google Scholar
Granger, C.W.J. (1983). Co-integrated variables and error-correcting models. Discussion Paper, 83–13, University of California, San Diego.Google Scholar
Granger, C.W.J. & Teräsvirta, T. (1993). Modelling nonlinear economic relationships. Oxford University Press.CrossRefGoogle Scholar
Hamilton, J.D. (1994). Time series analysis. Princeton University Press, Princeton, N.J.CrossRefGoogle Scholar
Hardy, M.R. (1993). Stochastic simulation in life office solvency assessment. J.I.A. 120, 131–151.Google Scholar
Hardy, M.R. (1994). Incorporating individual company variation in simulated equity returns. Transactions of the 4th International AFIR Colloquium, Orlando, 3, 1147–1162.Google Scholar
Harvey, A.C. (1989). Forecasting, structural time series models and the Kalman filter. Cambridge University Press.Google Scholar
Homer, S. (1963). A history of interest rates: 2000 B.C. to the present. Rutgers University Press, New Brunswick.Google Scholar
Hua, V. (1994). Modelling equity returns using a simple ARCH model. Transactions of the 4th International AFIR Colloquium, Orlando, 2, 537–565.Google Scholar
Huber, P.P. (1995). A review of Wilkie's stochastic investment model. Actuarial Research Paper No. 70, City University, London.Google Scholar
Hürlimann, W. (1993). Numerical evaluation of the Wilkie inflation model. Insurance: Mathematics & Economics, 11, 311–314.Google Scholar
Ibbotson, R.G. & Sinquefield, R.A. (1989). Stocks, bonds, bills and inflation: historical returns (1926–1987). The Research Foundation of the Institute of Chartered Financial Analysts, Charlottesville, Virginia.Google Scholar
Ingersoll, J.E. Jr, (1987). Theory of financial decision making. Rowman & Littlefield, Totowa, N.J.Google Scholar
Janicki, A. & Weron, A. (1994). Simulation and chaotic behaviour of astable stochastic processes. Marcel Dekker Inc, New York.Google Scholar
Jarque, C.M. & Bera, A.K. (1981). An efficient large sample test for normality of observations and regression residuals. Working papers in Economics and Econometrics, No. 47. Australian National University.Google Scholar
Johansen, S. & Juselius, K. (1990). Maximum likelihood estimation and inference on cointegration — with applications to the demand for money. Oxford Bulletin of Economics and Statistics, 52, 169–210.CrossRefGoogle Scholar
Johnson, M.E. (1987). Multivariate statistical simulation. John Wiley, New York.CrossRefGoogle Scholar
Johnson, N.L. & Kotz, S. (1970). Continuous univariate distributions. Houghton Mifflin, Boston.Google Scholar
Karatzas, I. & Shreve, S.E. (1991). Brownian motion and stochastic calculus. Second edition, Springer-Verlag, New York.Google Scholar
Kendall, Maurice Sir & Stuart, A. (1977). The advanced theory of statistics. Volume 1, Fourth edition, Charles Griffin, London.Google Scholar
Kitts, A. (1988). Applications of stochastic financial models: a review. Department of Social Statistics, University of Southampton.Google Scholar
Kitts, A. (1990). Comments on a model of retail price inflation. J.I.A. 117, 407–412.Google Scholar
Macdonald, A.S. (1991). On investment strategies using the Wilkie model. Proceedings of the 2nd AFIR International Colloquium, Brighton, 3, 413–427.Google Scholar
Macdonald, A.S. (1993). What is the value of a valuation? Transactions of the 3rd International AFIR Colloquium, Rome, 2, 723–743.Google Scholar
Macdonald, A.S. (1994). Appraising life office valuations. Transactions of the 4th International AFIR Colloquium, Orlando, 3, 1163–1183.Google Scholar
Macdonald, A.S. (1995). A stochastic evaluation of solvency valuations for life offices. Ph.D. Thesis, Heriot-Watt University, Edinburgh.Google Scholar
McLeod, G. (1982). Box Jenkins in practice. Gwilym Jenkins & Partners Ltd, Lancaster.Google Scholar
Maddocks, N.E., Nisbet, M.J., Nisbet, R.M. & Blythe, S.P. (1991). Determinism and chaos in long financial series. Transactions of the 2nd AFIR International Colloquium, Brighton, 3, 267–283.Google Scholar
Maturity Guarantees Working Party (1980). Report of the Maturity Guarantees Working Party. J.I.A. 107, 101–212.Google Scholar
Metz, M. & Ort, M. (1993). Stochastic models for the Swiss consumer's price index and the cost of the adjustment of pensions to inflation for a pension fund. Transactions of the 3rd AFIR International Colloquium, Rome, 2, 789–806.Google Scholar
Mills, T.C. (1994). The econometric modelling of financial time series. Cambridge University Press.Google Scholar
Mitchell, B.R. (1975). European Historical Statistics. Macmillan Press, London.Google Scholar
Mitchell, B.R. & Deane, P. (1962). Abstract of British historical statistics. Cambridge University Press.Google Scholar
Mitchell, B.R. & Jones, H.G. (1971). Second abstract of British historical statistics. Cambridge University Press.Google Scholar
O.E.C.D. (monthly). Main economic indicators. O.E.C.D., Paris.Google Scholar
Ong, A. (1994). A stochastic model for Treasury bills; an extension to Wilkie's model. Actuarial Research Report No 68, City University, London.Google Scholar
Pedersen, H., Shiu, E. & Thorlacius, A. (1989). Arbitrage-free pricing of interest rate contingent claims. Transactions of the Society of Actuaries, 41, 231–265.Google Scholar
Pentikäinen, T., Bonsdorff, H., Pesonen, M., Rantala, J. & Ruohonen, M. (1989). Insurance solvency and financial strength. Insurance Publishing Company, Helsinki.Google Scholar
Pesaran, M.H. & Pesaran, B. (1991). Microfit 3.0 user manual. Oxford University Press.Google Scholar
Phelps Brown, E.H. & Hopkins, S.V. (1956). Seven centuries of the prices of consumables, compared with builder's wages. Economica, 23, 296–312.CrossRefGoogle Scholar
Praetz, P.D. (1972). The distribution of share price changes. Journal of Business, 45, 49–55.CrossRefGoogle Scholar
Priestley, M.B. (1988). Non-linear and non-stationary time series analysis. Academic Press, London.Google Scholar
Pukkila, T., Ranne, A. & Sarvamaa, S. (1994). On stochastic modelling of inflation. Transactions of the 4th International AFIR Colloquium, Orlando, 2, 589–608.Google Scholar
Purchase, D.E., Fine, A.E.M., Headdon, C.P.et al. (1989). Reflections on resilience: some considerations of mismatching tests, with particular reference to non-linked long-term insurance business. J.I.A. 116, 347–452.Google Scholar
Rao, B.B., Editor (1994). Cointegration for the applied economist. St Martin's Press, New York.Google Scholar
Ross, M.D. (1989). Modelling a with-profits life office. J.I.A. 116, 691–715.Google Scholar
Rubinstein, R.Y. (1981). Simulation and the Monte Carlo method. John Wiley, New York.CrossRefGoogle Scholar
Samorodnitsky, G. & Taqqu, M.S. (1994). Stochastic non-gaussian random processes. Chapman & Hall, New York.Google Scholar
Sharp, K.P. (1988). Stochastic models of interest rates. Transactions of the 23rd International Congress of Actuaries, Helsinki, 5, 247–261.Google Scholar
Solvency Working Party (1986). The solvency of life assurance companies. T.F.A. 39, 251–340.Google Scholar
Strang, G. (1980). Linear algebra and its applications. Second edition, Academic Press, New York.Google Scholar
Taylor, S. (1986). Modelling financial time series. John Wiley, Chichester.Google Scholar
Thomson, R.J. (1994). A stochastic investment model for actuarial use in South Africa. Presented to the 1994 Convention of the Actuarial Society of South Africa.Google Scholar
Tilley, J.A. (1990). A stochastic yield curve model for asset/liability simulation. Transactions of the 1st AFIR International Colloquium, Paris, 2, 65–80.Google Scholar
Tilley, J.A. (1993). Stochastic yield curve models. Seminar Proceedings of the Canadian Institute of Actuaries, 4, Toronto, 62–85.Google Scholar
Tilley, J.A. & Mueller, M. (1991). Managing interest rate risk for long liabilities. Transactions of the 2nd AFIR International Colloquium, Brighton, 1, 169–184.Google Scholar
Tong, H. (1990). Non-linear time series: a dynamical system approach. Clarendon Press, Oxford.CrossRefGoogle Scholar
Toutounchi, A. (1984). A comprehensive time-series analysis of the dividends and dividend yields of sectors of the Financial Times-Actuaries and the Standard and Poor's share indices. Ph.D. Thesis, Heriot-Watt University, Edinburgh.Google Scholar
Walter, C. (1990). Mise en évidence de distributions Lévy-stables et d'une structure fractable sur le marché de Paris. Transactions of the 1st AFIR International Colloquium, Paris, 3, 241–259.Google Scholar
Wilkie, A.D. (1981). Indexing long term contracts. J.I.A. 108, 299–360 and T.F.A. 38, 55–126.Google Scholar
Wilkie, A.D. (1986a). A stochastic investment model for actuarial use. T.F.A. 39, 341–403.Google Scholar
Wilkie, A.D. (1986b). Some applications of stochastic investment models. J.I.A.S.S. 29, 25–51.Google Scholar
Wilkie, A.D. (1987). Stochastic investment models — theory and applications. Insurance: Mathematics and Economics, 6, 65–83.Google Scholar
Wilkie, A.D. (1992). Stochastic investment models for XXIst Century actuaries. Transactions of the 24th International Congress of Actuaries, Montréal, 5, 119–137.Google Scholar
Wilkie, A.D. (1993). Can dividend yields predict share price changes? Transactions of the 3rd International AFIR Colloquium, Rome, 1, 335–347.Google Scholar
Wilkie, A.D. (1994a). A stochastic model for consumer price indices and exchange rates in several countries. Transactions of the 4th International AFIR Colloquium, Orlando, 2, 633–658.Google Scholar
Wilkie, A.D. (1994b). Keynote speech of Proceedings of the Investment Seminar. Seminar Proceedings of the Canadian Institute of Actuaries, 4, Toronto, 4–40.Google Scholar
Wilkie, A.D. (1995). The risk premium on ordinary shares. B.A.J., 1, 251–293.Google Scholar
Working, H. (1960). Note on the correlation of first differences of averages in a random chain. Econometrica, 28, 916–918. Reprinted in COOTNER, P.H., Editor (1964). The random character of stock market prices. MIT Press, Cambridge, Mass.CrossRefGoogle Scholar
Cairns, A.J.G. (1995). Uncertainty in the modelling process. Transactions of the 25th International Congress of Actuaries, 1, 67–94.Google Scholar
Chatfield, C. (1995). Model uncertainty, data mining and statistical inference. Journal of the Royal Statistical Society, Series A, 158, 419–466.CrossRefGoogle Scholar