A summary of ongoing research in SYRTO project - Petros Dellaportas. July, 2 2014
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A summary of ongoing research in SYRTO project - Petros Dellaportas. SYRTO Code Workshop Workshop on Systemic Risk Policy Issues for SYRTO (Bundesbank-ECB-ESRB) Head Office of Deustche Bundesbank, Guest House Frankfurt am Main - July, 2 2014
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A summary of ongoing research in SYRTO project - Petros Dellaportas. July, 2 2014
- 1. A summary of ongoing research in SYRTO project SYstemic Risk TOmography: Signals, Measurements, Transmission Channels, and Policy Interventions Petros Dellaportas Athens University of Economics and Business - Department of Statistics Joint work with Arakelian, Plataniotis, Titsias, Savona, Vrontos SYRTO Code Workshop Workshop on Systemic Risk Policy Issues for SYRTO July, 22014 - Frankfurt (Bundesbank-ECB-ESRB)
- 2. Model 1: Copulas Model 2: Multivariate Stochastic volatility Model 3: A Bayesian factor model Model 4: Probability of Bank defaults Description of the data 5-year sovereign CDS of 7 countries in the euro area: France, Germany, Greece, Ireland, Italy, Portugal and Spain. Indices of banking and financial sector in Europe dates: January 1, 2008 to October 7, 2013.
- 3. Model 1: Copulas Model 2: Multivariate Stochastic volatility Model 3: A Bayesian factor model Model 4: Probability of Bank defaults CDS -all countries 04/02/08 08/15/09 12/28/10 05/11/12 09/23/13 0.5 1 1.5 2 2.5 x 10 4 France Germany Greece Ireland Italy Portugal Spain US
- 4. Model 1: Copulas Model 2: Multivariate Stochastic volatility Model 3: A Bayesian factor model Model 4: Probability of Bank defaults CDS -all countries without Greece 04/02/08 08/15/09 12/28/10 05/11/12 09/23/13 200 400 600 800 1000 1200 1400 1600 France Germany Ireland Italy Portugal Spain US
- 5. Model 1: Copulas Model 2: Multivariate Stochastic volatility Model 3: A Bayesian factor model Model 4: Probability of Bank defaults CDS - Greece 04/02/08 08/15/09 12/28/10 05/11/12 09/23/13 0.5 1 1.5 2 2.5 x 10 4 Greece
- 6. Model 1: Copulas Model 2: Multivariate Stochastic volatility Model 3: A Bayesian factor model Model 4: Probability of Bank defaults Dependencies via copulas For every pair of instruments we use the modelling approach of Arakelian and Dellaportas and construct a non-parametric estimate of their dependence (Kendal τ) across time this requires a computer-intensive parallel reversible jump MCMC algorithm for every pair
- 7. Model 1: Copulas Model 2: Multivariate Stochastic volatility Model 3: A Bayesian factor model Model 4: Probability of Bank defaults Greece 04/02/08 08/15/09 12/28/10 05/11/12 09/23/13 0 0.1 0.2 0.3 0.4 0.5 0.6 GrGer GrFr GrIr GrIt GrPort GrSp
- 8. Model 1: Copulas Model 2: Multivariate Stochastic volatility Model 3: A Bayesian factor model Model 4: Probability of Bank defaults Spain 2008 2009 2010 2012 2013 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 SpFr SpGer SpGr SpIr SpIt SpPort
- 9. Model 1: Copulas Model 2: Multivariate Stochastic volatility Model 3: A Bayesian factor model Model 4: Probability of Bank defaults Germany 04/02/08 08/15/09 12/28/10 05/11/12 09/23/13 0.1 0.2 0.3 0.4 0.5 0.6 GerFr GerGr GerIr GerIt GerPort GerSp
- 10. Model 1: Copulas Model 2: Multivariate Stochastic volatility Model 3: A Bayesian factor model Model 4: Probability of Bank defaults Italy 04/02/08 08/15/09 12/28/10 05/11/12 09/23/13 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 ItFr ItGer ItGr ItIr ItPort ItSp
- 11. Model 1: Copulas Model 2: Multivariate Stochastic volatility Model 3: A Bayesian factor model Model 4: Probability of Bank defaults Ireland 04/02/08 08/15/09 12/28/10 05/11/12 09/23/13 0.1 0.2 0.3 0.4 0.5 0.6 0.7 IrGr IrGer IrFr IrIt IrPort IrSp
- 12. Model 1: Copulas Model 2: Multivariate Stochastic volatility Model 3: A Bayesian factor model Model 4: Probability of Bank defaults Portugal 04/02/08 08/15/09 12/28/10 05/11/12 09/23/13 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 PortFr PortGer PortGr PortIr PortIt PortSp
- 13. Model 1: Copulas Model 2: Multivariate Stochastic volatility Model 3: A Bayesian factor model Model 4: Probability of Bank defaults Current research Treat all bivariate dependencies (estimated Kendal τ’s) as time series Investigate forecasting and dependencies possible avenue: Bayesian factor models. The assumption of normal errors in the response is obviously wrong so we need some clever modelling. Factors could be dependencies between Greece-Portugal-Ireland dependencies between Germany-France-Italy-Spain dependencies between the bank and financial indices inter-dependencies between the groups above
- 14. Model 1: Copulas Model 2: Multivariate Stochastic volatility Model 3: A Bayesian factor model Model 4: Probability of Bank defaults Description of the data 600 stocks from European index Available stock information (sector, market)
- 15. Model 1: Copulas Model 2: Multivariate Stochastic volatility Model 3: A Bayesian factor model Model 4: Probability of Bank defaults Dynamic eigenvalue and eigenvector modelling We decompose the covariance matrix at time t Σt = Pt Λt PT t and model Λt and Pt with an AR(1) process. Since Pt is a rotation matrix, it can be parameterised w.r.t. N(N − 1)/2 Givens angles, each one belonging to matrix Gjt: Pt = N(N−1) 2 j=1 Gjt The problem depends on a a very demanding MCMC algorithm. It works well with some very efficient proposal densities.
- 16. Model 1: Copulas Model 2: Multivariate Stochastic volatility Model 3: A Bayesian factor model Model 4: Probability of Bank defaults A factor model that reduces the dimension of the problem yt = Lft + t , t ∼ N (0, σ 2 IN ) where yt ∈ RN is the vector of log returns at time t, L ∈ RN×K is a sparse fixed matrix of factor loadings. L may consist of dummy variables that specify sectors and countries. The latent variable ft ∈ RK follows the MSV model, i.e. ft ∼ N (0, Σt )
- 17. Model 1: Copulas Model 2: Multivariate Stochastic volatility Model 3: A Bayesian factor model Model 4: Probability of Bank defaults The model r j it = a j i + b j it v j t + e j it b j it = b j 0i + φ j i (b j it−1 − b j 0i ) + A G j t + µ j it v j t = a j 0 + a j 1Vt + ω j t Vt = B Xt + ut j sectors (Sovereign, Banks and FinancialIntermediaries, Corporations) i financial assets (CDs and equity returns) r: returns v: sector systemic risk G,X: covariates V: macro-systemic risk factor
- 18. Model 1: Copulas Model 2: Multivariate Stochastic volatility Model 3: A Bayesian factor model Model 4: Probability of Bank defaults The model use of balance sheets and market data of bank stocks of the European index calculate financial ratios and estimate the debt of the bank Use the multivariate stochastic volatility model above Estimate the probability that the Asset value is smaller than the debt
- 19. This project has received funding from the European Union’s Seventh Framework Programme for research, technological development and demonstration under grant agreement n° 320270 www.syrtoproject.eu This document reflects only the author’s views. The European Union is not liable for any use that may be made of the information contained therein.