A Comparison of Actuarial Financial Scenario Generators Kevin C. Ahlgrim, ASA, MAAA, Ph.D. Department of Finance, Insurance and Law Illinois State University 340 College of Business Campus Box 5480 Normal, IL 61790-5480 USA 01-309-438-2727 [email protected] Stephen P. D’Arcy, FCAS, MAAA, Ph.D. Department of Finance University of Illinois at Urbana-Champaign 340 Wohlers Hall 1206 S. Sixth Street Champaign, IL 61820 USA 01-217-333-0772 [email protected] Richard W. Gorvett, FCAS, MAAA, ARM, FRM, Ph.D. Departments of Mathematics and Finance University of Illinois at Urbana-Champaign 273 Altgeld Hall 1409 West Green Street Urbana, IL 61801 USA 01-217-244-1739 [email protected] Acknowledgement: The authors wish to thank the Casualty Actuarial Society and the Society of Actuaries for sponsoring the original financial scenario research project, as well as the various members of the committees of both societies who provided detailed reviews and numerous excellent comments.A Comparison of Actuarial Financial Scenario Generators Abstract The actuarial profession is encouraging significant work on the modeling of asset returns and other economic and financial processes, with a view toward supporting Risk-Based Capital analysis, Dynamic Financial Analysis, pricing embedded options, solvency testing and other financial applications. One such recent study is the CAS-SoA research project on Modeling of Economic Series Coordinated with Interest Rate Scenarios. The American Academy of Actuaries also recently released a set of 10,000 prepackaged scenarios for common asset classes in support of the C-3 Phase 2 RBC for Variable Annuities. Both data sets provide practitioners with a large number of iterations for key financial values, including short- and long-term interest rates and equity returns. This paper provides a comparison of the underlying models and the outputs of these studies, to facilitate their understanding and use. JEL Classification: G22 Financial Economics – Insurance Keywords: Interest rates, equity returns, asset returns, economic scenarios, financial scenarios1. Introduction In May, 2001, the Casualty Actuarial Society (CAS) and the Society of Actuaries (SoA) jointly issued a request for proposals on the research topic “Modeling of Economic Series Coordinated with Interest Rate Scenarios.” The objectives of this request were to develop a research relationship with selected persons to investigate this topic; produce a literature review of work previously done in the area of economic scenario modeling; determine appropriate data sources and methodologies to enhance economic modeling efforts relevant to the actuarial profession; and produce a working model of economic series, coordinated with interest rates, that could be made public and used by actuaries via the CAS/SoA websites to project future economic scenarios. Categories of economic series to be modeled included interest rates, equity price levels, inflation rates, unemployment rates, and real estate price levels. In addition to providing the financial scenario generator model, this project also produced a set of output scenarios for these economic series that could be used directly in financial analysis. This work is summarized in Ahlgrim et al (2005). The Life Capital Adequacy Subcommittee of the American Academy of Actuaries recommended in a series of reports (December 2002, September 2003, and November 2003) that life insurers implement new tests of capital adequacy utilizing stochastic models for scenario testing of variable products with guarantees. Although the ultimate recommendation is for each insurer to develop its own models, the AAA was encouraged to provide 10,000 pre-packaged scenarios that could be used as an alternative. Practitioners are thus faced with a choice between two publicly available financial scenario generators. This paper will serve to explain the underlying processes used ineach set of models, compare the output values for common factors, and describe the issues that should be considered when using these models. The remainder of this paper is organized as follows. Section 2 describes the historical development of actuarial modeling of economic and financial processes, and places into perspective the current approaches involving stochastic modeling. Section 3 discusses the mathematical and economic details underlying each of the two publicly available financial scenario models. Section 4 analyzes and compares the results and outputs from each model. Section 5 illustrates the differences between the models via two simple examples of application. Section 6 concludes. 2. Stochastic Modeling Actuarial analysis has progressed through several stages of development regarding the use of economic variables. Initially, the standard approach was to use deterministic values for interest rates, equity returns and other key financial variables. Judgment was used to estimate the range of expected outcomes and to value embedded options such as investment return and minimum benefit guarantees. This approach often led to underpricing some features of insurance policies and consequent financial difficulties for a number of insurers, due in part to inadequate reflection of the potential risk and volatility associated with economic and financial processes. The uncertainty surrounding economic variables then began to be formally recognized by the use of predetermined scenarios that reflected specific economic conditions. For example, New York regulation 126 requires insurers to test asset adequacy, and assess their resulting hypothetical financial conditions, under sevenprescribed interest rate scenarios. Although an improvement over the deterministic approach, the use of a limited number of scenarios provided no indication of the relative frequency of any particular outcome, and did not reflect the full range of economic conditions that could be expected to occur. The latest stage in actuarial analysis has been the development of stochastic models to reflect the underlying uncertainty of economic and financial variables (Wilkie, 1986 and 1995, Hibbert, Mowbray and Turnbull, 2001). Properly developed economic models can be used to more accurately price embedded options in insurance contracts, to set appropriate solvency margins for diverse insurance operations and to evaluate alternative operational choices within an insurer.