Economic Scenario Generators Research Articles

On the dynamics of treasury bond yields: From term structure modelling to economic scenario generation

On the dynamics of treasury bond yields: From term structure modelling to economic scenario generation

On the benefits of pension plan consolidation: Understanding the impact of full plan mergers

Abstract This study investigates the benefits and drawbacks of pension plan consolidation by quantifying the impact of mergers of heterogeneous plans on different stakeholders in a unique Canadian implementation of defined benefit plans. Using a comprehensive framework that combines a realistic economic scenario generator, a stochastic mortality model that captures differences among subpopulations, a cost model with economies of scale, and a dynamic asset allocation methodology, we evaluate the combined effect of asset- and liability-side changes on three groups of measures: plan-related risk measures assessing profits from an economic capital perspective, consumption-based metrics to understand the impact on members, and contribution risk measures capturing the risk from the employer’s viewpoint. We apply the framework to a hypothetical and empirically relevant merger and find that consolidation is favorable under most circumstances: the positive impacts of better diversification and economies of scale continue to outweigh the negative effects of heterogeneity even when the merging plans have different mortality expectations, different maturity levels, or modest differences in initial funded ratios.

On stochastic modelling of actuarial compensation for loss of future earnings in Turkey

Abstract This article presents an actuarial perspective to estimate the economic loss for compensations resulting from a wrongful act. The main aim of this study is to propose a stochastic approach for modelling discount rates and survival probabilities which are used to calculate the present value of the future loss of earnings. We adopted the Wilkie model as an economic scenario generator to forecast future stochastic discount rates and fitted the Lee–Carter and the Heligman–Pollard models to forecast future age-specific survival probabilities using Turkish data. We discussed the impact of stochastic modelling on annuity values and compensation amounts through sensitivity analyses. We also compared the compensation amounts for various cases with the benchmark case representing current practice in Turkey. The results show that the compensation amounts are substantially affected by the financial assumptions, particularly in the case of an unstable economy. The major finding is that the uncertainty in future mortality rates is largely outweighed by the uncertainty associated with future financial and economic variables in the Turkish case.

An economic scenario generator for embedded derivatives in South Africa

It is well known that interest rate risk is a dominating factor when pricing long-dated contingent claims. The Heston stochastic volatility model fails to capture this risk as the model assumes a constant interest rate throughout the life of the claim. To overcome this, the risk-free interest rate can be modelled by a Hull-White short rate process and can be combined with the Heston stochastic volatility model to form the so-called Heston-Hull-White model. The Heston-Hull-White model allows for correlation between the equity and interest rate processes, a component that is important when pricing long-dated contingent claims. In this paper, we apply the Heston-Hull-White model to price Guaranteed Minimum Maturity Benefits (GMMBs) and Guaranteed Minimum Death Benefits (GMDBs) offered in the life insurance industry in South Africa. We propose a further extension by including stochastic mortality rates based on either a continuous-time Cox-Ingersoll-Ross short rate process or a discrete-time AR(1)-ARCH(1) model. Our findings suggest that stochastic interest rates are the dominating factor when reserving for GMMB and GMDB products. Furthermore, a delta-hedging strategy can help reduce the variability of embedded derivative liabilities.

Scenario Generation for Market Risk Models Using Generative Neural Networks

In this research study, we show how existing approaches of using generative adversarial networks (GANs) as economic scenario generators (ESG) can be extended to an entire internal market risk model—with enough risk factors to model the full band-width of investments for an insurance company and for a time horizon of one year, as required in Solvency 2. We demonstrate that the results of a GAN-based internal model are similar to regulatory-approved internal models in Europe. Therefore, GAN-based models can be seen as an alternative data-driven method for market risk modeling.

Economic Scenario Generators: a risk management tool for insurance

Economic Scenario Generators: a risk management tool for insurance

Ensemble Economic Scenario Generators: Unity Makes Strength

Over the last 40 years, various frameworks have been proposed to model economic and financial variables relevant to actuaries. These models are helpful, but searching for a unique model that gives optimal forecasting performance can be frustrating and ultimately futile. This study therefore investigates whether we can create better, more reliable economic scenario generators by combining them. We first consider eight prominent economic scenario generators and apply Bayesian estimation techniques to them, thus allowing us to account for parameter uncertainty. We then rely on predictive distribution stacking to obtain optimal model weights that prescribe how the models should be averaged. The weights are constructed in a leave-future-out fashion to build truly out-of-sample forecasts. An extensive empirical study based on three economies—the United States, Canada, and the United Kingdom—and data from 1992 to 2021 is performed. We find that the optimal weights change over time and differ from one economy to another. The out-of-sample behavior of the ensemble model compares favorably to the other eight models: the ensemble model’s performance is substantially better than that of the worse models and comparable to that of the better models. Creating ensembles is thus beneficial from an out-of-sample perspective because it allows for robust and reasonable forecasts.

ON COMPLEX ECONOMIC SCENARIO GENERATORS: IS LESS MORE?

AbstractThis article proposes a complex economic scenario generator that nests versions of well-known actuarial frameworks. The generator estimation relies on the Bayesian paradigm and accounts for both model and parameter uncertainty via Markov chain Monte Carlo methods. So, to the questionis less more?, we answer maybe, but it depends on your criteria. From an in-sample fit perspective, on the one hand, a complex economic scenario generator seems better. From the conservatism, forecasting and coverage perspectives, on the other hand, the situation is less clear: having more complex models for the short rate, term structure and stock index returns is clearly beneficial. However, that is not the case for inflation and the dividend yield.

FAIR TRANSITION FROM DEFINED BENEFIT TO TARGET BENEFIT

AbstractTarget benefit (TB) plans that incorporate intergenerational risk sharing have been demonstrated to be welfare improving over the long term. However, there has been little discussion of the short-term benefits for members in a defined benefit (DB) plan that is transitioning to TB. In this paper, we adopt a two-step approach that is designed to ensure the long-term sustainability of the new plan, without unduly sacrificing the benefit security of current retirees. We propose a cohort-based transition plan for reducing intergenerational inequity. Our study is based on simulations using an economic scenario generator with some theoretical results under simplified settings.

How can an economic scenario generation model cope with abrupt changes in financial markets?

PurposeIt is quite possible that financial institutions including life insurance companies would encounter turbulent situations such as the COVID-19 pandemic before policies mature. Constructing models that can generate scenarios for major assets to cover abrupt changes in financial markets is thus essential for the financial institution's risk management.Design/methodology/approachThe key issues in such modeling include how to manage the large number of risk factors involved, how to model the dynamics of chosen or derived factors and how to incorporate relations among these factors. The authors propose the orthogonal ARMA–GARCH (autoregressive moving-average–generalized autoregressive conditional heteroskedasticity) approach to tackle these issues. The constructed economic scenario generation (ESG) models pass the backtests covering the period from the beginning of 2018 to the end of May 2020, which includes the turbulent situations caused by COVID-19.FindingsThe backtesting covering the turbulent period of COVID-19, along with fan charts and comparisons on simulated and historical statistics, validates our approach.Originality/valueThis paper is the first one that attempts to generate complex long-term economic scenarios for a large-scale portfolio from its large dimensional covariance matrix estimated by the orthogonal ARMA–GARCH model.

Market efficiency and random number generators in Solvency II

Complex insurance policies are valued by Economic Scenario Generators (ESG), stochastic simulations developed via Monte Carlo techniques that span the evolution of risk factors important for insurers (financial and technical) consistent with market data. The either pseudo or quasi-random number generators used in the model turn out to be important for the precision of the valuation of Asset/Liability models. I shall compare five different random number generators in a G[Formula: see text] model in terms of market efficiency, by testing for the fulfilment of the martingale condition. The enhancement of existing methods is crucial in the field of computational insurance based on Monte Carlo techniques given that the number of simulations is perilously limited.

Do Jumps Matter in the Long Term? A Tale of Two Horizons

Economic scenario generators (ESGs) for equities are important components of the valuation and risk management process of life insurance and pension plans. Because the resulting liabilities are very long-lived and the short-term performance of the assets backing these liabilities may trigger important losses, it is thus a desired feature of an ESG to replicate equity returns over such horizons. In light of this horizon duality, we investigate the relevance of jumps in ESGs to replicate dynamics over different horizons and compare their performance to popular models in actuarial science. We show that jump-diffusion models cannot replicate higher moments if estimated with the maximum likelihood. Using a generalized method of moments–based approach, however, we find that simple jump-diffusion models have an excellent fit overall (moments and the entire distribution) at different timescales. We also investigate three typical applications: the value of $1 accumulated with no intermediate monitoring, a solvency analysis with frequent monitoring, and a dynamic portfolio problem. We find that jumps have long-lasting effects that are difficult to replicate otherwise, so, yes, jumps do matter in the long term.

Using a stochastic economic scenario generator to analyse uncertain superannuation and retirement outcomes

AbstractThe retirement systems in many developed countries have been increasingly moving from defined benefit towards defined contribution system. In defined contribution systems, financial and longevity risks are shifted from pension providers to retirees. In this paper, we use a probabilistic approach to analyse the uncertainty associated with superannuation accumulation and decumulation. We apply an economic scenario generator called the Simulation of Uncertainty for Pension Analysis (SUPA) model to project uncertain future financial and economic variables. This multi-factor stochastic investment model, based on the Monte Carlo method, allows us to obtain the probability distribution of possible outcomes regarding the superannuation accumulation and decumulation phases, such as relevant percentiles. We present two examples to demonstrate the implementation of the SUPA model for the uncertainties during both phases under the current superannuation and Age Pension policy, and test two superannuation policy reforms suggested by the Grattan Institute.

Personalised drawdown strategies and partial annuitisation to mitigate longevity risk

Despite the importance of drawdown strategies under a defined contribution system with increased longevity risk, little guidance to retired and retiring members has been forthcoming from superannuation funds. This paper provides a do-it-yourself drawdown design for members of superannuation funds along with comparison studies on a range of retirement income strategies under an array of realistic scenarios. A stochastic economic scenario generator is used to simulate the uncertain outcomes of different drawdown strategies during retirement. The impact of annuitisation for mitigating longevity risk under government pension rules and the selection of personalised drawdown and annuitisation strategies for retirement are examined.

A Practical Stochastic Model for Projecting Nominal Interest Rates in a Monte Carlo Setting

We present a real-world stochastic projection of nominal interest rate curves intended to integrate with Monte Carlo economic scenario generators. The model projects three time-varying parameters arising from a singular value decomposition of transformed historic interest rates, rather than modelling tenor points directly. A key feature is that we devise an empirically-motivated, rather than an assumed convenient form, transform function to apply to interest rates before performing the decomposition. This choice reflects an observed relationship between the volatility and level of interest rates. The resulting time-varying parameters, which we call time components, are projected as mean-reverting arithmetic random walks with mean reversion strength calibrated to historic behaviour. The drift of the model is adjusted so that the mean average of discount factors across simulations is in line with initial market-implied expectations. This adjustment preserves the required relationship between the level and the volatility of interest rates.

A graphical model approach to simulating economic variables over long horizons

AbstractWe present an application of statistical graphical models to simulate economic variables for the purpose of risk calculations over long time horizons. We show that this approach is relatively easy to implement, and argue that it is appealing because of the transparent yet flexible means of achieving dimension reduction when many variables must be modelled. Using the United Kingdom data as an example, we demonstrate the development of an economic scenario generator that can be used by life insurance companies and pension funds.We compare different algorithms to select a graphical model, based on p-values, AIC, BIC and deviance. We find the economic scenario generator to yield reasonable results and relatively stable structures in our example, suggesting that it would be beneficial for actuaries to include graphical models in their toolkit.

How to Define the Quality of an Economic Scenario Generator to Assess the Best-Estimate of a French Savings Contract in €?

Applying a Mark-to-Market approach to evaluate the fair value of the insurer’s commitment (best-estimate) for a saving French contract in €, implies having the prices of options and guarantees of insurance policies. Since this information is not observable on an organized and liquid market, the calculation is made in a Markto-Model framework. The calibration and validation of the economic scenario generator (ESG), used to evaluate the best-estimate, by comparing the simulations to the observed data as part of a statistical approach, cannot be considered. The ESG is then calibrated and validated with reference to the financial instruments (caps, floors, swaptions, etc.), derived from the modelled risk factors, without justifying a direct link or a bijection between these financial instruments and the liability options (see for example Laurent & al. [2014], Planchet & al. [2009], Armel & Planchet [2018]). The purpose of this paper is to examine how we can define the quality of an economic scenario generator to evaluate the best-estimate of French savings contracts in €.

Using Stochastic Economic Scenario Generators to Analyse Uncertain Superannuation Outcomes

The retirement systems in many developed countries have been increasingly moving from Defined Benefit (DB) towards the Defined Contribution (DC) system. In such systems, financial and longevity risks are shifted from the pension provider to the retiree. This paper uses a probabilistic approach to analyse the uncertainty associated with the retirement accumulation and decumulation in a DC world. We use an economic scenario generator (ESG) called Simulation of Uncertainty for Pension Analysis (SUPA) to project uncertain future economic outcomes. As the retirement system in Australia is predominantly DC in nature, and to validate the accuracy of the SUPA model, we use a unique dataset of over five million Australian individuals over ten years obtained from the Australian Department of Human Services (DHS) to benchmark the effectiveness of the SUPA model for simulating the superannuation accumulation phase of individuals. Our probabilistic approach allows us to estimate various outcomes regarding the retirement accumulation and decumulation phases, such as worst-case percentiles accounting for the risks associated with investment returns and other economic variables. In particular, our approach provides an advanced tool to analyse the sustainability of popular drawdown strategies during retirement under the current pension and superannuation scheme.

ECONOMIC SCENARIO GENERATOR AND PARAMETER UNCERTAINTY: A BAYESIAN APPROACH

AbstractIn 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.

Updating Wilkie's Economic Scenario Generator for U.S. Applications

The Wilkie economic scenario generator has had a significant influence on economic scenario generators (ESGs) since the first formal publication in Wilkie (1986). In this paper we update the model parameters using U.S.data to 2014, and review the model performance. In particular, we consider stationarity assumptions, parameter stability, and structural breaks.