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A graphical model approach to simulating economic variables over long horizons

Published online by Cambridge University Press:  12 July 2019

Jaideep S. Oberoi ,
Aniketh Pittea  and
Pradip Tapadar Open the ORCID record for Pradip Tapadar [Opens in a new window]
Jaideep S. Oberoi
Affiliation:
Kent Business School, University of Kent, Canterbury CT2 7FS, UK
Aniketh Pittea
Affiliation:
School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury CT2 7FS, UK
Pradip Tapadar*
Affiliation:
School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury CT2 7FS, UK
*
*Corresponding author. Email: [email protected]
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Abstract

We present an application of statistical graphical models to simulate economic variables for the purpose of risk calculations over long time horizons. We show that this approach is relatively easy to implement, and argue that it is appealing because of the transparent yet flexible means of achieving dimension reduction when many variables must be modelled. Using the United Kingdom data as an example, we demonstrate the development of an economic scenario generator that can be used by life insurance companies and pension funds.We compare different algorithms to select a graphical model, based on p-values, AIC, BIC and deviance. We find the economic scenario generator to yield reasonable results and relatively stable structures in our example, suggesting that it would be beneficial for actuaries to include graphical models in their toolkit.

Keywords

Graphical modelsscenario generatorsdimension reductionlong-term risk management
Type
Paper
Information
Annals of Actuarial Science , Volume 14 , Issue 1 , March 2020 , pp. 20 - 41
Copyright
© Institute and Faculty of Actuaries 2019 

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References

Ahlgrim, K.C., Stephen, P.D., Richard, W.G. & FRM, ARM (2004). Modeling of economic series coordinated with interest rate scenarios. Casualty Actuarial Society and the Society of Actuaries. https://www.casact.org/research/econ/section1.pdf Google Scholar
Ahlgrim, K.C., Stephen, P.D. & Richard, W.G. (2005). Modeling financial scenarios: A framework for the actuarial profession. In Proceedings of the Casualty Actuarial Society, vol. 92, pp. 177–238. Phoenix, Arizona.Google Scholar
Ang, A. & Piazzesi, M. (2003). A no-arbitrage vector autoregression of term structure dynamics with macroeconomic and latent variables. Journal of Monetary Economics, 50(4), 745–787.CrossRefGoogle Scholar
Campbell, J.Y. & Ammer, J. (1993). What moves the stock and bond markets? A variance decomposition for long-term asset returns. The Journal of Finance, 48(1), 3–37.CrossRefGoogle Scholar
Chan, W.-S. (2002). Stochastic investment modelling: a multiple time-series approach. British Actuarial Journal, 8(3), 545–591.CrossRefGoogle Scholar
Christoffersen, P.F. & Diebold, F.X. (2000). How relevant is volatility forecasting for financial risk management? Review of Economics and Statistics, 82(1), 12–22.CrossRefGoogle Scholar
Csardi, G. & Nepusz, T. (2006). The igraph software package for complex network research. InterJournal, Complex Systems, 1695. Available online at the address http://igraph.org.Google Scholar
Dethlefsen, C. & Højsgaard, S. (2005). A common platform for graphical models in R: The gRbase package. Journal of Statistical Software, 14(17), 1–12. Available online at the address http://www.jstatsoft.org/v14/i17/.CrossRefGoogle Scholar
Drton, M. & Perlman, M.D. (2007). Multiple testing and error control in Gaussian graphical model selection. Statistical Science, 22(3), 430–449.CrossRefGoogle Scholar
Drton, M. & Perlman, M.D. (2008). A SINful approach to Gaussian graphical model selection. Journal of Statistical Planning and Inference, 138, 1179–1200.CrossRefGoogle Scholar
Drton, M. & Maathuis, M.H. (2017). Structure learning in graphical modeling. Annual Review of Statistics and Its Application, 4, 365–393.CrossRefGoogle Scholar
Edwards, D. (2012). Introduction to Graphical Modelling. New York: Springer Science & Business Media.Google Scholar
Gentry, J., Gentleman, R. & Huber, W. (2010). How to Plot a Graph Using Rgraphviz. Available online at the address http://www.bioconductor.org/packages/release/bioc/vignettes/Rgraphviz/inst/doc/Rgraphviz.pdf.Google Scholar
Gibberd, A.J. & Roy, S. (2017). Multiple changepoint estimation in high-dimensional Gaussian graphical models. arXiv preprint arXiv:1712.05786.Google Scholar
Højsgaard, S., Edwards, D. & Lauritzen, S. (2012). Graphical Models with R. New York: Springer Science & Business Media.10.1007/978-1-4614-2299-0CrossRefGoogle Scholar
Huber, P.P. (1997). A review of Wilkie’s stochastic asset model. British Actuarial Journal, 3(1), 181–210.CrossRefGoogle Scholar
Jondeau, E. & Rockinger, M. (2006). The copula-garch model of conditional dependencies: An international stock market application. Journal of International Money and Finance, 25(5), 827–853.10.1016/j.jimonfin.2006.04.007CrossRefGoogle Scholar
Mulvey, J.M. & Thorlacius, A.E. (1998). The Towers Perrin global capital market scenario generation system. In Ziemba, W. & Mulvey, J. (Eds.), Worldwide Asset and Liability Modeling. Cambridge: Cambridge University Press.Google Scholar
Mulvey, J.M., Gould, G. & Morgan, C. (2000). An asset and liability management system for Towers Perrin–Tillinghast. Interfaces, 30(1), 96–114.CrossRefGoogle Scholar
Nyman, H., Pensar, J. & Corander, J. (2017). Stratified Gaussian graphical models. Communications in Statistics – Theory and Methods, 46(11), 5556–5578. doi:10.1080/03610926.2015.1105979. Available online at the address https://doi.org/10.1080/03610926.2015.1105979.CrossRefGoogle Scholar
Pedersen, H., Campbell, M.P., Christiansen, S.L., Cox, S.H., Finn, D., Griffin, K., Hooker, N., Lightwood, M., Sonlin, S.M. & Suchar, C. (2016). Economic scenario generators: A practical guide, technical report, Society of Actuaries. Available online at the address https://www.soa.org/research-reports/2016/2016-economic-scenario-generators/.Google Scholar
Porteous, B.T. (1995). How to Fit and Use a Stochastic Investment Model. Faculty of Actuaries Students’ Society Paper.Google Scholar
Porteous, B.T. & Tapadar, P. (2005). Economic Capital and Financial Risk Management for Financial Services Firms and Conglomerates. New York: Palgrave Macmillan.Google Scholar
Porteous, B.T. & Tapadar, P. (2008a). Asset allocation to optimise life insurance annuity firm economic capital and risk adjusted performance. Annals of Actuarial Science, 3, 187–214.10.1017/S1748499500000506CrossRefGoogle Scholar
Porteous, B.T. & Tapadar, P. (2008b). The impact of capital structure on economic capital and risk adjusted performance. ASTIN Bulletin, 38, 341–380.10.1017/S0515036100015191CrossRefGoogle Scholar
Porteous, B.T., Tapadar, P. & Yang, W. (2012). Economic capital for defined benefit pension schemes: An application to the UK universities superannuation scheme. Journal of Pension Economics and Finance, 11, 471–499.CrossRefGoogle Scholar
R Core Team. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. Available online at the address https://www.R-project.org.Google Scholar
Runge, J. (2013). On the graph-theoretical interpretation of Pearson correlations in a multivariate process and a novel partial correlation measure. arXiv preprint arXiv:1310.5169.Google Scholar
Smith, A.D. (1996). How actuaries can use financial economics. British Actuarial Journal, 2(5), 1057–1193.CrossRefGoogle Scholar
Thomson, R.J. & Gott, D.V. (2009). Stochastic models for actuarial use: the equilibrium modelling of local markets. ASTIN Bulletin: The Journal of the IAA, 39(1), 339–370.10.2143/AST.39.1.2038068CrossRefGoogle Scholar
Whitten, S.P. & Thomas, R.G. (1999). A non-linear stochastic asset model for actuarial use. British Actuarial Journal, 5(5), 919–953.CrossRefGoogle Scholar
Wilkie, A.D. (1986). A stochastic investment model for actuarial use. Transactions of the Faculty of Actuaries, 39, 341–381.10.1017/S0071368600009009CrossRefGoogle Scholar
Wilkie, A.D. (1995). More on a stochastic asset model for actuarial use. British Actuarial Journal, 1, 771–964.CrossRefGoogle Scholar
Wilkie, A.D. & ¸Sahin, ¸S (2016). Yet more on a stochastic economic model: part 2: initial conditions, select periods and neutralising parameters. Annals of Actuarial Science, 10(1), 1–51.CrossRefGoogle Scholar
Wilkie, A.D. & ¸Sahin, ¸S. (2017a). Yet more on a stochastic economic model: Part 3a: stochastic interpolation: Brownian and ornsteinuhlenbeck (ou) bridges. Annals of Actuarial Science, 11(1), 74–99.CrossRefGoogle Scholar
Wilkie, A.D. & ¸Sahin, ¸S (2017b). Yet more on a stochastic economic model: Part 3b: stochastic bridging for retail prices and wages. Annals of Actuarial Science, 11(1), 100–127.10.1017/S174849951600021XCrossRefGoogle Scholar
Wilkie, A.D. & ¸Sahin, ¸S. (2017c). Yet more on a stochastic economic model: Part 3c: stochastic bridging for share yields and dividends and interest rates. Annals of Actuarial Science, 11(1), 128–163.CrossRefGoogle Scholar
Wilkie, A.D. & ¸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(1), 67–105. doi:10.1017/S1748499517000112. Available online at the address https://doi.org/10.1017/S1748499517000112.CrossRefGoogle Scholar
Wilkie, A.D. & ¸Sahin, ¸S. (2019). Yet more on a stochastic economic model: Part 5: a vector autoregressive (var) model for retail prices and wages. Annals of Actuarial Science, 13(1) 92–108. Cambridge University Press. doi:10.1017/S1748499518000106.Google Scholar
Wilkie, A.D., ¸Sahin, ¸S., Cairns, A.J.G. & Kleinow, T. (2011). Yet more on a stochastic economic model: Part 1: updating and refitting, 1995 to 2009. Annals of Actuarial Science, 5, 53–99.CrossRefGoogle Scholar
Wolstenholme, R.J. & Walden, A.T. (2015). An efficient approach to graphical modeling of time series. IEEE Transactions on Signal Processing, 63(12), 3266–3276.CrossRefGoogle Scholar
Yakoubov, Y.H., Teeger, M.H. & Duval, D.B. (1999). The TY model: A stochastic investment model for asset and liability management. Staple Inn Actuarial Society.Google Scholar
Yang, W. & Tapadar, P. (2015). Role of the pension protection fund in financial risk management of UK defined benefit pension sector: a multi-period economic capital study. Annals of Actuarial Science, 9, 134–166.CrossRefGoogle Scholar