Introduction Data Analysis VAR Regime Switching Multivariate RS Simulation Conclusion Economic Scenario Generation with Regime Switching Models Michael Sherris and Boqi Zhang UNSW Actuarial Research Seminar 2pm to 3pm Friday 22 May, ASB 115 Acknowledgement: Research funding from Taylor-Fry Research Grant and ARC Discovery Grant DP0663090 Michael Sherris and Boqi Zhang UNSW Actuarial Research Seminar Economic Scenario Generation with Regime Switching Models
Introduction Data Analysis VAR Regime Switching Multivariate RS Simulation Conclusion Presentation Overview Introduction, Background and ERCH Model Data, Descriptive Statistics and Other Tests Univariate AR Model and Vector Autoregression Model (VAR) Univariate Regime Switching RSAR(1) Model Multivariate Regime Switching RSVAR(1,2) Model Models Simulation Comparison and Conclusion Michael Sherris and Boqi Zhang UNSW Actuarial Research Seminar Economic Scenario Generation with Regime Switching Models
Introduction Data Analysis VAR Regime Switching Multivariate RS Simulation Conclusion Economic Scenario Generators Economics Scenario Generators increasingly used - life, non-life, superannuation; solvency, DFA, investment strategy ERCH model developed in Australia for life insurance solvency VAR models in economics and econometrics Regime switching models for univariate series - used by SoA for solvency, product guarantees for equity returns Multivariate regime switching model using the VAR model structure less well developed - issues with multivariate models (parsimony, data) Michael Sherris and Boqi Zhang UNSW Actuarial Research Seminar Economic Scenario Generation with Regime Switching Models
Introduction Data Analysis VAR Regime Switching Multivariate RS Simulation Conclusion ESG Models Early models - cascade structure,Box-Jenkins transfer function - Wilkie (1986, 1995) Development of commercial models - consultants: Towers Perrin CAP:Link; in-house DFA models; model specialists Barrie Hibbert; others Algorithmics etc Hamilton (1989, 1990) - regime switching Harris (1994) developed the Exponential Regressive Conditional Heteroscedasticity (ERCH) model Hardy (2001) - SoA solvency and products with guarantees Michael Sherris and Boqi Zhang UNSW Actuarial Research Seminar Economic Scenario Generation with Regime Switching Models
Introduction Data Analysis VAR Regime Switching Multivariate RS Simulation Conclusion ERCH Model m series ERCH model is expressed in multivariate form as X t = M + ΘΨ ∗ t + ξ t , ξ t = Λ t Z t ln Λ t = diag { ω 0 + ΩΦ t } Z t ∼ N (0 , Σ z ) � 0 , if t � = s , E ( Z T t Z s ) = Σ z , if t = s . where M = E ( X t ) is an m ∗ 1 column vector of unconditional series means, Θ is an m ∗ p conditional mean parameter matrix, Ψ t is a p ∗ 1 column vector of lagged explanatory variable values at time t , with the superscript asterix referring to unconditional mean adjustment so that Ψ ∗ t = Ψ t − E (Ψ t ) Michael Sherris and Boqi Zhang UNSW Actuarial Research Seminar Economic Scenario Generation with Regime Switching Models
Introduction Data Analysis VAR Regime Switching Multivariate RS Simulation Conclusion ERCH Model ξ t is an m ∗ 1 column vector of conditionally multivariate normal random errors or shocks to the series at time t , Λ t is an m ∗ m diagonal matrix of error standard deviations at time t , ln Λ t is an m ∗ m diagonal matrix of the logarithms of the error standard deviations at time t , Z t is an m ∗ 1 column vector of multivariate standard normal standardized error or shocks to the series at time t , diag { ... } is a diagonal matrix whose i -th non-zero element is equal to the i -th element of its vector arguments Michael Sherris and Boqi Zhang UNSW Actuarial Research Seminar Economic Scenario Generation with Regime Switching Models
Introduction Data Analysis VAR Regime Switching Multivariate RS Simulation Conclusion ERCH Model ω 0 is an m ∗ 1 column vector of parameters, Ω is an m ∗ q conditional volatility parameter matrix, Φ t is a q ∗ 1 column vector of lagged explanatory variable values at time t . Σ z is an m ∗ m contemporaneous correlation matrix, the i , j th element of which is equal to the contemporaneous correlation between the i th and jth components of the Z t , Harris (1994) estimated parameters based on quarterly Australian data. Michael Sherris and Boqi Zhang UNSW Actuarial Research Seminar Economic Scenario Generation with Regime Switching Models
Introduction Data Analysis VAR Regime Switching Multivariate RS Simulation Conclusion Data Data used for fitting the models is from Reserve Bank of Australia (RBA), the Australia Bureau of Statistics (ABS) and Residex for their residential house index series. Quarterly data for all the following 11 series are taken from these sources and has been modelled in the form of difference of log value. The sample period is from the first quarter of 1979 to the third quarter of 2006. There are 111 quarterly observations for each economic series or 111 ∗ 11 = 1221 data points in total. Michael Sherris and Boqi Zhang UNSW Actuarial Research Seminar Economic Scenario Generation with Regime Switching Models
Introduction Data Analysis VAR Regime Switching Multivariate RS Simulation Conclusion Data Plots Variable Description G t the log return of GDP the log return of CPI F t R t the log return adjusted SPI (Share Price Index of ASX 200) the log return of Dividend of the adjusted SPI Y t T t the log return of 90-day Treasury notes yield B 2 t the log return of 2-year Treasury Bond yield B 10 t the log return of 10-year Treasury Bond yield the log return of average weekly earnings AWE t UR t the log return of unemployment rate RESH t the log return of residential house index in Sydney USB 2 t the log return of US 2-year Treasury Bond yield Michael Sherris and Boqi Zhang UNSW Actuarial Research Seminar Economic Scenario Generation with Regime Switching Models
Introduction Data Analysis VAR Regime Switching Multivariate RS Simulation Conclusion Plot in log return of GDP 0.04 lnGDP 0.03 0.02 0.01 log return % 0 −0.01 −0.02 −0.03 0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96100 104 108 111 Quarter Michael Sherris and Boqi Zhang UNSW Actuarial Research Seminar Economic Scenario Generation with Regime Switching Models
Introduction Data Analysis VAR Regime Switching Multivariate RS Simulation Conclusion Plot in log return of CPI 0.045 logCPI 0.04 0.035 0.03 0.025 log return % 0.02 0.015 0.01 0.005 0 −0.005 0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96 100104 108 111 Quarter Michael Sherris and Boqi Zhang UNSW Actuarial Research Seminar Economic Scenario Generation with Regime Switching Models
Introduction Data Analysis VAR Regime Switching Multivariate RS Simulation Conclusion Plot in log return of SPI and its Dvd 0.3 lnSPI lnDvd 0.2 0.1 0 log return % −0.1 −0.2 −0.3 −0.4 −0.5 −0.6 0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96 100 104 108 111 Quarter Michael Sherris and Boqi Zhang UNSW Actuarial Research Seminar Economic Scenario Generation with Regime Switching Models
Introduction Data Analysis VAR Regime Switching Multivariate RS Simulation Conclusion Plot in log return of AUD interest rates 0.5 log 90−day T−note log 2−year T−bond 0.4 log 10−year T−bond 0.3 0.2 log return % 0.1 0 −0.1 −0.2 −0.3 0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96 100104108 111 Quarter Michael Sherris and Boqi Zhang UNSW Actuarial Research Seminar Economic Scenario Generation with Regime Switching Models
Introduction Data Analysis VAR Regime Switching Multivariate RS Simulation Conclusion Plot in log return of AWE 0.05 log AWE 0.04 0.03 log return % 0.02 0.01 0 −0.01 −0.02 0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96 100104108 111 Quarter Michael Sherris and Boqi Zhang UNSW Actuarial Research Seminar Economic Scenario Generation with Regime Switching Models
Introduction Data Analysis VAR Regime Switching Multivariate RS Simulation Conclusion Plot in log return of Unemployment Rate 0.25 log Unemployment Rate 0.2 0.15 0.1 log return 0.05 0 −0.05 −0.1 0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96 100104108 111 Quarter Michael Sherris and Boqi Zhang UNSW Actuarial Research Seminar Economic Scenario Generation with Regime Switching Models
Introduction Data Analysis VAR Regime Switching Multivariate RS Simulation Conclusion Plot in log return of Residential property price index 0.1 log RESH 0.08 0.06 0.04 log return 0.02 0 −0.02 −0.04 0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96 100104108 111 Quarter Michael Sherris and Boqi Zhang UNSW Actuarial Research Seminar Economic Scenario Generation with Regime Switching Models
Introduction Data Analysis VAR Regime Switching Multivariate RS Simulation Conclusion Plot in log return of 2year US interest rate 0.6 log US 2−year T−bond 0.4 0.2 0 log return −0.2 −0.4 −0.6 −0.8 0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96 100104108 111 Quarter Michael Sherris and Boqi Zhang UNSW Actuarial Research Seminar Economic Scenario Generation with Regime Switching Models
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