Economic Scenario Generator and Parameter Uncertainty: A Bayesian Approach

Abstract

In this article, we study parameter uncertainty and its actuarial implications in the context of economic scenario generators. To account for this additional source of uncertainty in a consistent manner, we cast Wilkie’s four-factor framework into a Bayesian model. The posterior distribution of the model parameters is estimated using Markov chain Monte Carlo methods and is used to perform Bayesian predictions on the future values of the inflation rate, the dividend yield, the dividend index return and the long-term interest rate. According to the US data, parameter uncertainty has a significant impact on the dispersion of the four economic variables of Wilkie’s framework. The impact of such parameter uncertainty is then assessed for a portfolio of annuities: the right tail of the loss distribution is significantly heavier when parameters are assumed random and when this uncertainty is estimated in a consistent manner. The risk measures on the loss variable computed with parameter uncertainty are at least 12% larger than their deterministic counterparts.

On Complex Economic Scenario Generators: Is Less More?

“…Nonetheless, it also includes the potential for heteroscedasticity (i.e., Equation (2.3)) and σ 2 q,t is the time-t conditional variance of the inflation. The variance is updated via a GARCH model similar to those used by Kilian and Manganelli (2007) and Bégin (2016) in the context of inflation modelling. The long-run variance level of the inflation rate is given by σ 2 q , and α q , β q and γ q are the reaction, persistence and asymmetry parameters, respectively.…”

“…J. -F. BÉGIN 1984-F. BÉGIN 1986-F. BÉGIN 1988-F. BÉGIN 1990-F. BÉGIN 1992-F. BÉGIN 1994-F. BÉGIN 1996-F. BÉGIN 1998-F. BÉGIN 2000-F. BÉGIN 2002-F. BÉGIN 2004-F. BÉGIN 2006-F. BÉGIN 2008-F. BÉGIN 2010-F. BÉGIN 2012-F. BÉGIN 2014-F. BÉGIN 2016 Third, the monthly term structure of risk-free interest rates is based upon the Federal Reserve Board's H.15 release and obtained via the Wharton Research Data Service. This study focuses on 3-month and 1-, 2-, 3-, 5-, 7-, 10-, and 30-year interest rates.…”

“…Similar to the results of Section 4, cumulative inflation rates are larger for M 4 , leading to more significant lower and upper bounds for this model (see Panel A of Table 4). As both very low and very high inflation rates can be problematic for insurers (Bégin, 2016), it is unclear whether one model would be more conservative than the others from an inflation perspective.…”

“…Based on the Box-Jenkins approach, his framework is composed of four connected models: an inflation model, an interest rate model, a dividend yield model and a stock index return model. It has been the object of multiple studies over the years (e.g., Geoghegan et al, 1992;Wilkie, 1995;Huber, 1997;Zhang et al, 2018;Bégin, 2019).…”

“…The notion of parameter uncertainty, on the one hand, is not a new concern for actuaries and has been studied on multiple occasions; for instance, see Hartman et al (2017) and references therein for a general review, and Bégin (2019) for an application to ESGs. Model uncertainty, on the other hand, has been less of a consideration.…”