Simulation of Long-term Returns with Stochastic Correlations

Document Type : Original Article


1 Department of Mathematics, Statistics and Computer Science, University of Bergamo, Via dei Caniana, 24127 Bergamo, Italy (Corresponding author)

2 Department of Mathematics, Statistics and Computer Science, University of Bergamo, Via dei Caniana, 24127 Bergamo, Italy


This paper focuses on a nonlinear stochastic model for financial simulation and forecasting based on assumptions of multivariate stochastic correlation, with an application to the European market. We present in particular the key elements of a structured hierarchical econometric model that can be used to forecast financial and commodity markets relying on statistical and simulation methods. The investment universe includes money-market, fixed-income, inflation-linked bonds as well as equity and commodity indices. For each such investment opportunity a dedicated statistical model has been developed to generate future return paths describing the uncertainty the investment manager is facing over time.


1)     Arbeleche, S., & Dempster, M. A. H. (2003). Econometric modelling for global asset liability management. Working Paper, Centre for Financial Research, University of Cambridge, in preparation.
2)     Bauwens, L., Laurent S., & Rombouts J. V. K. (2006). Multivariate GARCH models: a survey. Journal of applied econometrics, 21(1), 79-109.
3)     Cappiello, L., Engle, R. F., & Sheppard, K. (2006). Asymmetric dynamics in the correlations of global equity and bond returns. Journal of Financial econometrics, 4(4), 537-572.
4)     Consigli, G., & Dempster, M. A. H. (1998). Dynamic stochastic programming for asset-liability management. Annals of Operations Research, 81, 131-162.
5)     Consigli, G., di Tria, M., Gaffo, M., Iaquinta, G., Moriggia, V., & Uristani, A. (2011). Dynamic portfolio management for property and casualty insurance. In Stochastic Optimization Methods in Finance and Energy (pp. 99-124). Springer New York.
6)     Consigli, G., Iaquinta, G., Moriggia, V., di Tria, M., & Musitelli, D. (2012). Retirement planning in individual asset-liability management. IMA Journal of Management Mathematics, 23(4), 365-396.
7)     Consigli, G., Iaquinta, G., & Moriggia, V. (2012). Path-dependent scenario trees for multistage stochastic programmes in finance. Quantitative Finance, 12(8), 1265-1281.
8)     Cox, J. C., Ingersoll Jr, J. E., & Ross, S. A. (1985). A theory of the term structure of interest rates. Econometrica: Journal of the Econometric Society, 385-407.
9)     D’Ecclesia, R. L. (2017). Time Varying Correlation: a Key Indicator in Finance. In Consigli G., Stefani S. & Zambruno G., editors, Recent advances in Commodity and Financial Modeling: Quantitative methods in Banking, Finance, Insurance, Energy and Commodity markets. International Series in Operations Research and Management Science. Springer, forthcoming.
10)  Dempster, M. A. H., Germano, M., Medova, E. A., Murphy, J. K., Ryan, D., & Sandrini, F. (2009). Risk profiling defined benefit pension schemes. To appear in: Journal of Portfolio Management.
11)  Dempster, M. A., Germano, M., Medova, E. A., & Villaverde, M. (2003). Global asset liability management. British Actuarial Journal, 9(01), 137-195.
12)  Engle, R. (2002). Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models. Journal of Business & Economic Statistics, 20(3), 339-350.
13)  Engle, R. (2009). Anticipating correlations: a new paradigm for risk management. Princeton University Press.
14)  Engle, R. F., & Patton, A. J. (2001). What good is a volatility model. Quantitative finance, 1(2), 237-245.
15)  Engle, R., & Figlewski, S. (2015). Modeling the dynamics of correlations among implied volatilities. Review of Finance, 19(3), 991-1018.
16)  Engle, R. F., & Sheppard, K. (2001). Theoretical and empirical properties of dynamic conditional correlation multivariate GARCH (No. w8554). National Bureau of Economic Research.
17)  Glasserman, P. (2003). Monte Carlo methods in financial engineering (Vol. 53). Springer Science & Business Media.
18)  Glosten, L. R., Jagannathan, R., & Runkle, D. E. (1993). On the relation between the expected value and the volatility of the nominal excess return on stocks. The journal of finance, 48(5), 1779-1801.
19)  Hafner, C. M., & Franses, P. H. (2009). A generalized dynamic conditional correlation model: simulation and application to many assets. Econometric Reviews, 28(6), 612-631.
20)  Kim, S., Shephard, N., Chib, S. (1998). Stochastic volatility: likelihood inference and comparison with ARCH models. The review of economic studies, 65(3), 361-393.
21)  Mulvey, J. M. (1996). Generating scenarios for the Towers Perrin investment system. Interfaces, 26(2), 115.
22)  Pesaran, B., & Pesaran, M. H. (2007). Modelling volatilities and conditional correlations in futures markets with a multivariate t distribution.
23)  Silvennoinen, A., & Thorp, S. (2013). Financialization, crisis and commodity correlation dynamics. Journal of International Financial Markets, Institutions and Money, 24, 42-65.
24)  Zakoian, J. M. (1994). Threshold heteroskedastic models. Journal of Economic Dynamics and control, 18(5), 931-955