Improving Longevity and Mortality Risk Models with Common Stochastic Long-Run Trends

Modeling Long-Run Cause of Death Mortality Trends

Longevity risk is among the most important factors to consider for pricing and risk management of longevity products. Past improvements in mortality over many years, and the uncertainty of these improvements, have attracted the attention of experts, both practitioners and academics. Since aggregate mortality rates reflect underlying trends in causes of death, insurers and demographers are increasingly considering cause-of-death data to better understand risks in their mortality assumptions. The relative importance of causes of death has changed over many years. As one cause reduces, others increase or decrease. The dependence between mortality for different causes of death is important when projecting future mortality. However, for scenario analysis based on causes of death, the assumption usually made is that causes of death are independent. Recent models, in the form of Vector Error Correction Models (VECMs), have been developed for multivariate dynamic systems and capture time dependency with common stochastic trends. These models include long-run stationary relations between the variables and thus allow a better understanding of the nature of this dependence. This article applies VECMs to cause-of-death mortality rates to assess the dependence between these competing risks. We analyze the five main causes of death in Switzerland. Our analysis confirms the existence of a long-run stationary relationship between these five causes. This estimated relationship is then used to forecast mortality rates, which are shown to be an improvement over forecasts from more traditional ARIMA processes, which do not allow for cause-of-death dependencies.

In this article, we develop strategies of hedging multiyear mortality (longevity) risk for a life insurer (an annuity provider) through purchasing some mortality-linked securities from a financial intermediary. Under the multiyear hedges for a life insurer (an annuity provider) involving two uncertain factors—the mortality rate and the number of life insureds (annuity recipients)—we derive closed-form formulas for the optimal units of purchasing underlying mortality-linked securities. Numerical illustrations show that the downside risk of loss because of mortality (longevity) risk for the life insurer (annuity provider) can be significantly hedged by purchasing the optimal units of mortality-linked securities, and the sample risk can be reduced by increasing the number of life insureds (annuity recipients) at issue. For a financial intermediary, adopting an optimal weight of a portfolio of life and annuity business can reduce extreme losses from the longevity risk but could slightly increase losses from the mortality risk, and the sample risk cannot necessarily be eliminated by increasing the number of life insureds/annuity recipients at issue.

How strongly are foreign exchange markets linked in terms of their similarities in long-run fluctuations? Are they cointegrating? To analyze such “comovements,” we present a time-varying cointegration model for the foreign exchange rates of the currencies of Canada, Japan, and the UK vis-à-vis the U.S. dollar from May 1990 through July 2015. Unlike previous studies, we allow the loading matrix in the vector error-correction (VEC) model to be varying over time. Because the loading matrix in the VEC model is associated with the speed at which deviations from the long-run relationship disappear, we propose a new degree of market comovement based on the time-varying loading matrix to measure the strength or robustness of the long-run relationship over time. Since exchange rates are determined by macrovariables, cointegration among exchange rates implies these variables share common stochastic trends. Therefore, the proposed degree measures the degree of market comovement. Our main finding is that the market comovement has become stronger over the past quarter-century, but at a decreasing rate with two major turning points: one in 1995 and the other one in 2008.

Cumulative Sum Curves and Their Prediction Limits

This research aims to predict the mortality rates of Malaysian sub-populations in thirteen different states using the Three-Way Lee-Carter model: the extended version of the Lee-Carter model. This model considers the coherence characteristic between subpopulations as it allows combination estimates of the three variables: i) time, ii) age and iii) different subpopulations, which is useful to assess the magnitude of mortality differential between subpopulations. The Three-Way Lee-Carter model has never been tested using Malaysian mortality rates, particularly to forecast mortality of subpopulations in different states. Hence this research predicts the thirteen-state populations' mortality rates and compares the model's performance to the original Lee-Carter model. The collected data includes mortality rates by age, gender, and states obtained from the Department of Statistics Malaysia from 1991 until 2018. Results show that the Three-Way Lee-Carter model successfully fits into the Malaysia data better than the original Lee-Carter model. In terms of out-sample forecasts, the Three-Way Lee-Carter model outperforms the Lee-Carter model for eight subpopulations including for Kelantan males, Perlis males, Sabah males, Terengganu males, Perak females, Perlis females, Sarawak females and Selangor females.

Purpose This paper investigates the impact of exchange rate movements on firm value, settling a long-standing argument on the magnitude of its effect. We aim to shed light on the mystery of exchange rate exposure. Design/methodology/approach An analysis of monthly data for ten (10) years from 1st April 2012 to 31st March 2022 for 567 import and export-oriented Indian firms has been undertaken. Econometric models like auto-regressive integrated moving average (ARIMA), vector error correction model (VECM), and autoregressive distributed lag (ARDL) have been used to derive the unanticipated component of the exchange rate to estimate for each firm separately using ordinary least squares. Findings The study has found that 80.95% (459/567) of the sample firms have exhibited significant exposure to unanticipated exchange rate changes derived from the ARIMA model. The level of exposure varies from 74.56% to 54.85% using several other models and different exchange rate measures. Research limitations/implications The study found, confirmed and emphasised the various possible reasons for the ongoing debate of the “Exchange Rate Exposure Puzzle.” An approach for measuring exchange rate exposure has been suggested. Financial managers may use the recommended method to measure exchange rate exposure. Originality/value The study has added value to the existing literature by arguing that measurement bias committed by the existing literature is primarily due to the usage of actual exchange rates and argues how unanticipated exchange rate changes are an effective and superior measurement tool for exchange rate exposure.

It is demonstrated how the techniques of unit root testing and cointegration may be used to test for common stochastic trends, and their implications for addressing the market efficiency hypothesis (MEH) in a multivariate context within a seven-variable system of major daily (unpublished) spot exchange rates of the Malaysian ringgit. Finding the evidence of two cointegrating vectors, a vector error-correction model is developed to test for the direction of temporal causal dynamics (in the Granger sense) within this system before investigating the relative strength of the causality by decomposing the total impact of an unanticipated shock to each of the variables beyond the sample period, into proportions attributable to shocks in the other variables including its own. Results from the analysis tend to suggest a violation of the MEH in a speculative sense, due to the presence of two cointegrating vectors which also withstood the temporal instability test. The VECM and decompositions of forecast error varia...

Operation safety and efficiency are two main concerns in power plants. It is important to detect the anomalies in power plants, and further judge whether they affect key performance indicators (KPIs), such as the thermal efficiency. These two goals can be achieved by KPI-related nonstationary process monitoring. Although the thermal efficiency cannot be accurately measured online, it can be strongly characterized by some online measurable variables, including the exhaust gas temperature and oxygen content of flue gas. These critical variables closely related to the thermal efficiency are termed as output variables. Inspired from nonstationary common trends between input and output variables in thermal power plants, the output-relevant common trend analysis (OCTA) method is proposed, in this article, to model the input–output relationship. In OCTA, input and output variables are decomposed into nonstationary common trends and stationary residuals, and the model parameters are estimated by solving an optimization problem. It is pointed out that OCTA is a generalized form of partial least squares (PLS). The superior monitoring performance of OCTA is illustrated by case studies on a real power plant in Zhejiang Provincial Energy Group of China. Compared with the other PLS-based recursive algorithms, OCTA can effectively detect the anomalies in power plants and accurately determine whether they have an impact on the thermal efficiency or not.

This paper uses a common trend model, following King et al. (Am Econ Rev 81:819–840, 1991), Mellander et al. (J Appl Econ 7(4):369–394, 1992), and Warne (A common trends model: identification, estimation and inference. Seminar Paper 555, Institute for International Economic Studies, Stockholm University, 1993), to evaluate, for 1994–2015, the role of the terms of trade vis-à-vis domestic productivity in explaining macroeconomic fluctuations in Peru. Our results show that Peru’s macroeconomic aggregates share two common trends: an external one, associated with the evolution of the terms of trade; and a domestic one, linked to the evolution of domestic productivity. The external common trend has a larger impact on private investment and public expenditure than on consumption and output, a result consistent with the role of investment in absorbing income volatility. The permanent terms of trade (foreign) shocks account for most of the volatility in output, consumption, private investment, and public expenditure. This result appears more pronounced as the time horizon approaches the long term.

A Multi-species modeling approach to consider the effects of environmental parameters on Caspian sturgeon fishes stock status

Multi-country risk management of longevity risk provides new opportunities to hedge mortality and interest rate risks in guaranteed lifetime income streams. This requires consideration of both interest rate and mortality risks in multiple countries. For this purpose, we develop value-based longevity indexes for multiple cohorts in two different countries that take into account the major sources of risks impacting life insurance portfolios, mortality and interest rates. To construct the indexes we propose a cohort-based affine model for multi-country mortality and use an arbitrage-free multi-country Nelson–Siegel model for the dynamics of interest rates. Index-based longevity hedging strategies have the advantages of efficiency, liquidity and lower cost but introduce basis risk. Graphical risk metrics are a way to effectively capture the relationship between an insurer's portfolio and hedging strategies. We illustrate the effectiveness of using a value-based index for longevity risk management between two countries using graphical basis risk metrics. To show the impact of both interest rate and mortality risk we use Australia and the UK as domestic and foreign countries, and, to show the impact of mortality only, we use the male populations of the Netherlands and France with common interest rates and basis risk arising only from differences in mortality risks.

Modeling and forecasting human mortality are significant research topics in several disciplines because mortality rates are fundamental in planning and policy decisions. Among various techniques, Lee Carter (LC) model is one of the most popular stochastic method in human mortality modeling. The original LC model was fuzzified to eliminate the assumptions related with homoscedasticity. The existing fuzzy model makes use of ordinary least squares (OLS) technique, which prevents the model to capture the existing fluctuations in data. In this study, a revised version of fuzzy LC model utilizing singular value decomposition (SVD) technique is proposed to overcome this issue. After modeling the mortality rates, their future values are forecasted by a modified first order fuzzy time series technique. For illustration purposes, proposed method is applied to mortality data of Finland. Numerical outputs show that proposed method is statistically better in modeling mortality compared to the existing fuzzy method. In addition, the modified fuzzy time series technique generates better forecasts than the original version.

The Lee–Carter model could be considered as one of the most important mortality prediction models among stochastic models in the field of mortality. With the recent developments of machine learning and deep learning, many studies have applied deep learning approaches to time series mortality rate predictions, but most of them only focus on a comparison between the Long Short-Term Memory and the traditional models. In this study, three different recurrent neural networks, Long Short-Term Memory, Bidirectional Long Short-Term Memory, and Gated Recurrent Unit, are proposed for the task of mortality rate prediction. Different from the standard country level mortality rate comparison, this study compares the three deep learning models and the classic Lee–Carter model on nine divisions’ yearly mortality data by gender from 1966 to 2015 in the United States. With the out-of-sample testing, we found that the Gated Recurrent Unit model showed better average MAE and RMSE values than the Lee–Carter model on 72.2% (13/18) and 67.7% (12/18) of the database, respectively, while the same measure for the Long Short-Term Memory model and Bidirectional Long Short-Term Memory model are 50%/38.9% (MAE/RMSE) and 61.1%/61.1% (MAE/RMSE), respectively. If we consider forecasting accuracy, computing expense, and interpretability, the Lee–Carter model with ARIMA exhibits the best overall performance, but the recurrent neural networks could also be good candidates for mortality forecasting for divisions in the United States.

Perhaps the most widely followed price in the market is the price of crude oil. The volatility of this commodity is evident to consumers through the gasoline prices that consumers see on the retail side. The U.S. Energy Information Agency provides widely followed forecasts for the retail gasoline price (along with other energy products) produced with their short-term energy outlook (STEO) model. The purpose of this research is to compare a number of forecasts using different techniques to the STEO model. This is accomplished through the use of Holt Winters, structural, ARIMA, and vector error-correction models. We also construct a composite forecast by averaging the respective forecasts from the four models. From the empirical analysis, we find evidence from the structural model and the vector error-correction model that the movement in the gasoline prices can be explained by the West Texas Intermediate (WTI) benchmark and the spread between BRENT and WTI benchmarks. In terms of forecasting performance, the additive Holt Winters model outperforms the other models within sample. Out sample, the composite forecast is the best performing model. The composite forecast has a MAPE of 6.3% versus a MAPE of 8.1% from the STEO model.