Casualty Actuarial Society Experienced Practitioner Pathway Seminar Lecture 6 – Current Issues – Economic Scenario Generators Stephen P. D’Arcy, FCAS, MAAA, Ph.D. Robitaille Chair of Risk and Insurance California State University – Fullerton D’Arcy Risk Consulting, Inc.

Overview Key aspect of any economic capital model is the approach used for the Economic Scenario Generator (ESG) What ESGs are available? What are the key differences among the ESGs? How do you select which ESG to use? EPP Lecture 6: Current Issues - Economic Scenario Generators

Economic Scenario Generators Stochastic models that can produce multiple potential financial variables that are consistent with each other Key variables modeled Interest rates Credit spreads Inflation rates Equity returns and dividend Real estate returns Unemployment rates Foreign exchange rates EPP Lecture 6: Current Issues - Economic Scenario Generators

Sources of Economic Scenario Generators Internally developed Public access Commercial products – some examples Barrie & Hibbert ESG Conning GEMS® Ortec Finance Dynamic Scenario Generator Towers Watson Star ESG EPP Lecture 6: Current Issues - Economic Scenario Generators

Internal Development Expect to invest multiple man and woman years into project Expertise required Modeling Economics and Finance Common sense Communication skills Advantages Geared to specific needs of company Someone in company truly understands the model Company owns the model Disadvantages Development time and initial cost Need to update continually Obtaining regulatory and rating agency acceptance EPP Lecture 6: Current Issues - Economic Scenario Generators

Public Access Models - 1 CAS Public Access DFA Model – Dynamo http://www.pinnacleactuaries.com/Products/dynamo/dynamoDownload.aspx CAS/SOA Financial Scenario Generator http://casact.org/research/econ/ American Academy of Actuaries Interest Rate and Equity Generators http://www.actuary.org/content/economic-scenario-generators#10 EPP Lecture 6: Current Issues - Economic Scenario Generators

CAS/SOA Model Modeled Economic Series Inflation Real Interest Rates Unemployment Nominal Interest Real Estate Stock Dividends Stock Returns EPP Lecture 6: Current Issues - Economic Scenario Generators

Public Access Models - 2 Advantages Disadvantages Cost Useful learning tools Disadvantages Generally not updated Developed for a specific purpose EPP Lecture 6: Current Issues - Economic Scenario Generators

Commercial Economic Scenario Generators - Examples Barrie & Hibbert ESG http://www.barrhibb.com/economic_scenario_generator Contact: Stephen Urbrock (stephen.urbrock@barrhibb.com) Conning GEMS® http://www.conning.com/risk-and-capital-management/software/gems.html Contact: Chris Suchar, chris.suchar@conning.com Ortec Finance Dynamic Scenario Generator http://global.ortec-finance.com/Pensions/Solutions/dynamic-scenario- generator.aspx Contact: André van Vliet, Andre.vanVliet@ortec-finance.com Towers Watson Star ESG http://www.towerswatson.com/en/Services/Tools/star-esg Contact: Jon Mossman, jonathan.mossman@towerswatson.com EPP Lecture 6: Current Issues - Economic Scenario Generators

Legal Disclaimer The CAS does not endorse any of the vendors mentioned in this presentation. The providers of the software products and services that are compared here operate entirely separately from each other and do not share information. EPP Lecture 6: Current Issues - Economic Scenario Generators

Barrie & Hibbert ESG No single Barrie & Hibbert ESG model User selects from a range of stochastic models Can provide model of 29 global economies including emerging markets Transparent and open Models taken from academic literature and leading practitioners Models and calibration fully documented and updated quarterly Now part of Moody’s Corporation Access to Moody’s Data Buffet platform Calibrations at the state and regional level for GDP and unemployment Cover entire fixed income structured finance space Moo EPP Lecture 6: Current Issues - Economic Scenario Generators

Barrie & Hibbert Basic Single-Economy ESG Structure Source – Barrie & Hibbert email communication EPP Lecture 6: Current Issues - Economic Scenario Generators

Barrie & Hibbert Interest Rate Models Extended Black-Karasinski Model Two-factor arbitrage free model Lognormal – cannot produce negative values Used for nominal interest rates Libor Market Model Vasicek Model One-factor model Normal – can produce negative values Used for real interest rates EPP Lecture 6: Current Issues - Economic Scenario Generators

Historical 3-month Nominal Rates and Model Project Distribution – Dec Source – Barrie & Hibbert Insurance Economic Scenario Generator Modeling Suite, Page 9 EPP Lecture 6: Current Issues - Economic Scenario Generators

Barrie & Hibbert Inflation Model Model nominal and real interest rates Derive inflation rates Mean reverting process with time dependent varying reversion level EPP Lecture 6: Current Issues - Economic Scenario Generators

Barrie & Hibbert Equity Models Log-normal model – constant volatility Deterministic volatility model Local volatility model Stochastic volatility jump diffusion model Equity mean reversion model EPP Lecture 6: Current Issues - Economic Scenario Generators

Conning GEMS® Economic Scenario Generator Open and transparent 16 correlated economies Innovative Academically rigorous Utilizes the most up-to-date research Empirically demonstrable Relationships fully accounted for within and across economies Extensively tested and validated EPP Lecture 6: Current Issues - Economic Scenario Generators

Conning GEMS® Economic Scenario Generator Interest Rates Credit Spreads Equity Returns Inflation, GDP, Unemployment Claim Cost Inflation Market Value and Cash Flows Municipal Bond Model Prepayments, etc. Credit Rating Transitions Corporate Security Model Corporate Yield Model EPP Lecture 6: Current Issues - Economic Scenario Generators

Conning GEMS® Overview of Primary Models EPP Lecture 6: Current Issues - Economic Scenario Generators

Conning GEMS® Projections at Year End 2008 EPP Lecture 6: Current Issues - Economic Scenario Generators

Conning GEMS® Inflation 4 factor affine model 3 factors from interest rate models 1 factor inflation index Model incorporates extreme scenarios including deflation EPP Lecture 6: Current Issues - Economic Scenario Generators

Ortec Finance Dynamic Scenario Generator (DSG) Provides consistent scenarios with monthly updates Scenarios include key aspects from literature and empirical data Term structure of risk and return Business cycle dynamics Stochastic volatility Tail risk (both within and between asset classes) Non-normal distributions Term structure dynamics Employs a combination of advanced quantitative techniques to meet its objectives EPP Lecture 6: Current Issues - Economic Scenario Generators

Ortec Finance DSG – Example Tail correlations Euro and US monthly equity returns EPP Lecture 6: Current Issues - Economic Scenario Generators

Ortec Finance DSG Frequency Domain Approach EPP Lecture 6: Current Issues - Economic Scenario Generators

Ortec Finance DSG Software and Calibrations EPP Lecture 6: Current Issues - Economic Scenario Generators

Ortec Finance DSG - Variable Coverage Currently around 350 variables (excluding client specific) EPP Lecture 6: Current Issues - Economic Scenario Generators

Ortec Finance DSG Backtest example Dec10 EPP Lecture 6: Current Issues - Economic Scenario Generators

Towers Watson Star ESG Fully coherent and integrated stochastic Monte Carlo generator Models 20 economies Fully transparent and documented Supports regulatory submissions Calibrated based on fitting the models to historical data and then adjusted to reflect the long-term views of the Towers Watson Global Investment Committee Updated quarterly Allows users to rescale economic scenarios to reflect the user’s views or create stochastic stress tests EPP Lecture 6: Current Issues - Economic Scenario Generators

Towers Watson Star ESG Nominal interest rates The Norman (2009) Real World Extension of the Libor Market Model. This model is also used, with minor adjustments, to model real yields and LIBOR spreads Inflation Linear function of current and past short-term interest rates and inflation Error term is AR(1) with conditional heteroskedasticity to give higher volatility in higher inflation environments Equity returns Geometric Brownian motion with jumps EPP Lecture 6: Current Issues - Economic Scenario Generators

Towers Watson Star ESG EPP Lecture 6: Current Issues - Economic Scenario Generators

Towers Watson Star ESG Inflation EPP Lecture 6: Current Issues - Economic Scenario Generators

Towers Watson Star Equity Returns EPP Lecture 6: Current Issues - Economic Scenario Generators

Comparing Economic Scenario Generators Reference: Ahlgrim, D’Arcy and Gorvett, 2008, A Comparison of Actuarial Scenario Generators, Variance Vol. 2, pp. 111-134. Compares the CAS/SoA model with the AAA C-3 Phase 2 Risk Based Capital model EPP Lecture 6: Current Issues - Economic Scenario Generators

Comparative Statistics: Interest Rates These statistics are during the first 20 years of projections EPP Lecture 6: Current Issues - Economic Scenario Generators

Histogram of 3 Month Nominal Interest Rates Model Values and Actual Data (01/34-01/06) Model allows users to reject negative interest rate scenarios EPP Lecture 6: Current Issues - Economic Scenario Generators

Funnel of Doubt Graphs 3 Month Nominal Interest Rates (U. S Funnel of Doubt Graphs 3 Month Nominal Interest Rates (U. S. Treasury Bills) EPP Lecture 6: Current Issues - Economic Scenario Generators

Histogram of Large Stock Return Model Values and Actual Data (1872-2006) EPP Lecture 6: Current Issues - Economic Scenario Generators

Comparative Statistics: Equity Returns CAS-SOA model has some extremes. But the “middle” of the distribution seems okay (under both) EPP Lecture 6: Current Issues - Economic Scenario Generators

Quantification of Model Fit Kolmogorov-Smirnov test Tries to determine if two datasets differ significantly Uses the maximum vertical difference between percentile plots of the data as statistic D Chi-square test Take the squared difference between observed frequency (O) and the expected frequency (E), and then divided by the expected frequency EPP Lecture 6: Current Issues - Economic Scenario Generators

Kolmogorov-Smirnov Test EPP Lecture 6: Current Issues - Economic Scenario Generators

Chi-square Test EPP Lecture 6: Current Issues - Economic Scenario Generators

Conclusions Selecting an ESG is a key component of many ERM quantitative analyses Significant differences in approaches to developing an ESG exist Develop a basic understanding of the approach used Examine output for reasonability Users often have better understanding of the real world than the modelers Tail values are critical as these will generate greatest financial stress Consider magnitude of extreme values Should be greater than historical experience – The worst is yet to come Should have reasonable probabilities in tails Review projections regularly Remember – you are not trying to fit the past, but to project the future EPP Lecture 6: Current Issues - Economic Scenario Generators