On the epidemic of financial crises

Demiris, Nikolaos and Kypraios, Theodore and Smith, L. Vanessa (2012): On the epidemic of financial crises.

Abstract

This paper proposes a framework for modelling financial contagion that is based on SIR (Susceptible-Infected-Recovered) transmission models from epidemic theory. This class of models addresses two important features of contagion modelling, which are a common shortcoming of most existing empirical approaches, namely the direct modelling of the inherent dependencies involved in the transmission mechanism, and an associated canonical measure of crisis severity. The proposed methodology naturally implies a control mechanism, which is required when evaluating prospective immunisation policies that intend to mitigate the impact of a crisis. It can be implemented not only as a way of learning from past experiences, but also at the onset of a contagious financial crisis. The approach is illustrated on a number of currency crisis episodes, using both historical final outcome and temporal data. The latter require the introduction of a novel hierarchical model that we call the Hidden Epidemic Model (HEM), and which embeds the stochastic financial epidemic as a latent process. The empirical results suggest, among others, an increasing trend for global transmission of currency crises over time.

• Item Type: MPRA Paper
• Language: English
• Keywords: Financial crisis, contagion, stochastic epidemic model, random graph, MCMC
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C11 - Bayesian Analysis: General; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C15 - Statistical Simulation Methods: General; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C51 - Model Construction and Estimation; G - Financial Economics > G0 - General > G01 - Financial Crises; G - Financial Economics > G1 - General Financial Markets > G15 - International Financial Markets

References

Addy, C. L., Longini, I. M. and Haber, M. (1991). A generalized stochastic model for the analysis of infectious disease final size data. Biometrics 47, 961-974.

Aït-Sahalia, Y., Cacho-Diaz, J.A. and R.J.A. Laeven (2010). Modeling financial contagion using mutually exciting processes. NBER Working Paper No. 15850.

Allen, F. and D. Gale (2000). Financial contagion. Journal of Political Economy 108, 1-33.

Amini, H., Cont, R. and A. Minca (2010). Resilience to contagion in financial networks. Mimeo.

Anderson, R. M., and R. M. May (1991). Infectious diseases of humans. Oxford, U.K.: Oxford University Press.

Andersson, H. and T. Britton (2000). Stochastic epidemic models and their statistical analysis. Lecture Notes in Statistics 151, Springer, New York.

Ball, F. G. (1986). A unified approach to the distribution of total size and total area under the trajectory of infectives in epidemic models. Adv. Appl. Probab. 18, 289-310.

Ball, F. G., Britton, T. and O. D. Lyne (2004). Stochastic multitype epidemics in a community of households: Estimation of threshold parameter R_{∗} and secure vaccination coverage. Biometrika, 91, 345-362.

Ball, F. and P. J. Donelly (1995). Strong approximations for epidemic models. Stochastic Processes and Applications, 55, 1-21.

Ball, F. G. and O. D. Lyne (2006). Optimal vaccination schemes for epidemics among a population of households, with application to variola minor in Brasil. Statistical Methods in Medical Research, 15, 481-487.

Ball, F.G., Mollison, D. and G. Scalia-Tomba (1997). Epidemics with two levels of mixing. Annals of Applied Probability 7, 46-89.

Balthrop, J., Forrest, S., Newman, M.E.J. and M.M. Williamson (2004). Technological networks and the spread of computer viruses. Science, 304, 527-529.

Banerjee, A.V. (1993). The economics of rumors. Review of Economic Studies 60, 309-327.

Barbour, A.D. and D. Mollison (1990). Epidemics and random graphs. In Stochastic Processes in epidemic theory, eds. Gabriel J. P. and Lefevre, C., Lecture notes in Biomathematics 86, 86-89.

Britton, T. (1998) Estimation in multitype epidemics. J. R. Statist. Soc. B 60, 993-679.

Britton, T. and N.G. Becker (2000). Estimating the immunity coverage required to prevent epidemics in a community of households. Biostatistics, 1, 389-402.

Brunetti, C., Scotti, C., Mariano, R. S. and A.H.H. Tan (2008). Markov switching GARCH models of currency turmoil in Southeast Asia. Emerging Markets Review 9, 104-128.

Calvo, G.A. and E.G. Mendoza (2000). Rational contagion and the globalization of securities markets. Journal of International Economics 55, 79-113.

Caporale, G.M., Serguieva, A. and H. Wu (2009). Financial contagion: evolutionary optimization of a multinational agent-based model. Intelligent Systems in Accounting, Finance and Management. Intell. Sys. Acc. Fin. Mgmt. 16, 111-125.

Caramazza, F., Ricci, L. and R. Salgado (2004). International financial contagion in currency crises. Journal of International Money and Finance 23, 51--70. Chang, R. and G. Majnoni (2001). International contagion: Implications for policy. In: Claessens, S., Forbes, K. (Eds), International Financial Contagion. Kluwer Academic Publishers.

Corsetti, G., Pesenti, P., Roubini, N. and C. Tille (1998). Structural links and contagion effects in the Asian crisis: A welfare based approach. New York, New York University.

Daley, D.J. and J. Gani (2000) Epidemic modelling: An introduction. Cambridge University Press, Cambridge, UK.

Dasgupta, A., Leon-Gonzalez, R. and A. Shortland (2011), Regionality revisited: An examination of the direction of spread of currency crises. Journal of International Money and Finance 30, 831-848.

De Gregorio, J. and R. Valdes (2001). Crisis transmission: Evidence from the debt, tequila and Asian flu crises. The World Bank Economic Review 15, 289-314.

Demiris, N. and P.D. O'Neill (2005a). Bayesian inference for stochastic multitype epidemics in structured populations via random graphs. Journal of the Royal Statistical Society Series B 67, 731-745.

Demiris, N. and P.D. O'Neill (2005b). Bayesian inference for epidemic models with two levels of mixing. Scand. J. Statist. 32, 265-280.

Diekmann, O. and J.A.P, Heesterbeek (2000). Mathematical epidemiology of infectious diseases: model building, analysis and interpretation. New York: Wiley.

Dietz, K. (1993). The estimation of the basic reproduction number for infectious diseases. Statistical Methods in Medical Research 2, 23-41.

Dornbusch, R., Park, Y.C. and S. Claessens (2000). Contagion: Understanding how it spreads. The World Bank Research Observer, 15, 177-197.

Dungey, M., Fry, R., González-Hermosillo, B. and V.L. Martin (2005). A comparison of alternative tests of contagion with applications. In Dungey, M. and D. Tambakis (eds), Identifying international financial contagion: Progress and challenges, Ch. 3, Oxford University Press, New York.

Dungey, M. and V.L. Martin (2007). Unravelling financial market linkages during crises. Journal of Applied Econometrics, 22, 89-119.

Eichengreen, B., Rose, A. and C. Wyplosz (1996). Contagious currency crises: First tests. Scandinavian Journal of Economics 98, 463-484.

Ethier, S.N. and T.G. Kurtz (1986). Markov Processes: Characterization and Convergence. Wiley, New York.

Forbes, K.J. and R. Rigobon (2002). No contagion, only interdependence: Measuring stock market comovements. Journal of Finance, 5, 2223-2261.

Foss, and T. Konstantopoulos. (2003) Extended renovation theory and limit theorems for stochastic ordered graphs. Markov Proc. Rel. Fields, 9, 413-468.

Frankel, J.A. and A.K. Rose (1996). Currency crashes in emerging markets: An empirical treatment. Journal of International Economics, 41, 351-366.

Fraser, C., Donnelly, C.A., Cauchemez, S., Hanage, W.P., Van Kerkhove, M.D., Hollingsworth, T.D., Griffin, J., Baggaley, R.F., Jenkins, H.E., Lyons, E.J., et al. (2009). Pandemic Potential of a Strain of Influenza A (H1N1) : Early Findings. Science, 324, 1557-1561.

Gai, P. and S. Kapadia (2010). Contagion in financial networks. Proc. Roy. Soc. A, vol. 466, no. 2120, 2401-2423. Geoffard, P.-Y. and T. Philipson (1997). Disease eradication: Private versus public vaccination. American Economic Review, 87, 222-230.

Gerlach, S. and F. Smets (1995). Contagious speculative attacks. European Journal of Political Economy 11, 45-63.

Gersovitz, M. and J. S. Hammer (2004). The economical control of infectious diseases. Economic Journal, 114, 1-27.

Glick, R. and A.K. Rose (1999). Contagion and trade: Why are currency crises regional? Journal of International Money and Finance 18, 603-617.

Gravelle, T., Kichian, M. and J. Morley (2006). Detecting shift-contagion in currency and bond markets. Journal of International Economics, 68, 409-423.

Green, P.J. (1995). Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika, 82, 711-732.

Haldane, A. (2009). Rethinking the Financial Network. www.bankofengland.co.uk/ publications/speeches/2009/speech386.pdf.

Haile, F. and S. Pozo (2008). Currency Crisis Contagion and the Identification of Transmission Channels. International Review of Economics and Finance 17, 572-588.

Jacobs, J.P.A.M., Kuper, G.H. and Lestano (2005). Identifying financial crises. In Dungey, M. and D. Tambakis (Eds), Identifying International Financial Contagion: Progress and Challenges, Oxford University Press, Oxford, 86-110.

Jewell, C.P., Kypraios, T., Neal, P. and G.O. Roberts (2009). Bayesian analysis for emerging infectious diseases. Bayesian Analysis, 4, 465-498.

Kaminsky, G.L. (2006). Currency crises: Are they all the same? Journal of International Money and Finance 25, 503-527.

Kaminsky, G.L and C.M. Reinhart (1998). Financial crises in Asia and Latin America: Then and now. American Economic Review 88, 444-448.

Kaminsky, G.L. and C.M. Reinhart (2000). On crises, contagion and confusion. Journal of International Economics 51, 145-168.

Kingman, J.F.C. (1993) Poisson processes. Oxford University Press.

Kodres, L.E. and M. Pritsker (2002). A rational expectations model of financial contagion. Journal of Finance, 57, 769-799.

Kosfeld, M. (2005). Rumours and markets. Journal of Mathematical Economics 41, 646-664.

Lefèvre, C. and Picard, P. (1990). A non-standard family of polynomials and the final size distribution of Reed--Frost epidemic processes. Adv. Appl. Prob. 22, 25-48.

Ludwig, D. (1975) Final size distributions for epidemics. Mathematical Biosciences 23, 33-46.

Mandilaras, A. and G. Bird (2010). A Markov switching analysis of contagion in the EMS. Journal of International Money and Finance, 29, 1062-1075.

Martinez Peria, M. S. (2002). A regime-switching approach to the study of speculative attacks: A focus on EMS crises. Empirical Economics, 27, 299-334.

May, R. M. and N. Arinaminpathy (2010). Systemic risk: the dynamics of model banking systems. J. R. Soc. Interface 7, 823-838.

May, R.M., Levin, S.A. and G. Sugihara (2008). Complex systems: Ecology for bankers, 451, 893-895.

Neal, P.J. (2006). Multitype randomised Reed-Frost epidemics and epidemics upon random graphs. Annals of Applied Probability 16, 1166-1189.

Nekovee, M., Moreno, Y., Bianconi, G. and M. Marsili (2007). Theory of rumour spreading in complex social networks. Physica A 374, 457-470.

Newman, M.E.J. (2010). Networks: An introduction. Oxford University Press.

O'Neill, P.D. (2009). Bayesian inference for stochastic multitype epidemics in structured populations using sample data. Biostatistics, 10, 779-791.

O'Neill, P.D. and G.O. Roberts (1999). Bayesian inference for partially observed stochastic epidemics. Journal of the Royal Statistical Society Series A 162, 121-129.

Pericoli, M. and M. Sbracia (2003). A primer on financial contagion. Journal of Economic Surveys, 17, 571-608.

Rida, W.N. (1991). Asymptotic properties of some estimators for the infection rate in the general stochastic epidemic model. J. Roy. Statist. Soc. B, 53, 269-283.

Sachs, J., Tornell, A. and A. Velasco (1996). Financial crises in emerging markets: The lessons from 1995. Brookings Paper 27, 147-199.

Scalia-Tomba G. (1985) Asymptotic final size distribution for some chain-binomial processes. Adv. Appl. Prob. 17, 477-495.

Shah, D. and T. Zaman (2011). Rumors in a network: Who's the culprit? IEEE Transactions on Information Theory, 57, 5163-5181.

Toxvaerdy, F. (2010). Infection, acquired immunity and externalities in treatment. Unpublished Manuscript. Faculty of Economics. University of Cambridge.

Van Rijckeghem, C., and B. Weder (2001), Sources of contagion: Is it finance or trade?, Journal of International Economics, 54, 293-308.