Assurance companies face two main risk factors in the process of pricing annuity products namely the interest risk and the longevity risk. There are numerous products and possibilities for the insurers to hedge their interest risk using interest derivatives and long bonds. Hedging products against the longevity risk is uncommon but insurers have to take it into account when they are pricing their annuity products.
There are two types of longevity risks. On the one hand the idiosyncratic longevity risk and on the other hand the systematic longevity risk. With regards to the idiosyncratic longevity risk, individuals are faced with the issue that they need to invest in assets for their retirement in spite of an uncertain span of lifetime and thus an uncertain investment horizon. Pricing of life annuities could be done according to corresponding mortality tables. If the clients of an insurer die on average according to mortality rates provided by such tables, the revenues of the insurer should be sufficient to ensure the payments for the clients who are still alive. The issue out of a pension fund perspective is that longevity has been improving over time and clients could live longer than anticipated. These improvements occurred in an unpredictable way, especially at higher ages according to Cairns et al. (2006). Insurers therefore made false calculations of the insurance premium and suffered losses due to pensioners living longer than anticipated.
The systematic longevity risk is based on the stochastic variation of mortality. The future development of life expectancy will be highly unpredictable due to medical improvements or discoveries in genetic research. For that reason insurers need stochastic models to quantify the systematic mortality changes over time and to make a prediction about future mortality in order to prevent losses caused by longevity risk.
This paper will firstly discuss the literature regarding the Lee and Carter one factor model and the relevance of longevity risk for annuity pricing. Second this paper aims to estimate the stochastic two-factor model by Cairns, Blake and Dowd (2006) (CBD) for U.S. males from 1933 to 2010 by running a simulation to predict average mortality for the year 2030. In the further course will this stated prediction be used to price an annuity product followed by a brief conclusion and summary of results.
Table of Contents
1 Introduction
2 Literature Review
3 Model Implementation
3.1 Estimation of A_1 and A_2
3.2 Prediction of A_1 and A_2
3.3 Predicted Mortality Rates for 2030
3.4 Pricing of an Immediate Pension Annuity
4 Conclusion
Objectives and Topics
The primary objective of this paper is to analyze longevity risk from a pension fund perspective by applying the stochastic two-factor model developed by Cairns, Blake, and Dowd (CBD). The paper aims to quantify systematic mortality changes and utilize these forecasts to price immediate pension annuities, thereby helping insurers mitigate potential losses from pensioners living longer than anticipated.
- Analysis of systematic versus idiosyncratic longevity risk.
- Evaluation of the Lee and Carter (1992) mortality forecasting model.
- Implementation of the CBD two-factor stochastic model using U.S. male mortality data (1933–2010).
- Simulation of future mortality rates for the year 2030.
- Pricing of lifetime annual income annuities under varying interest rate assumptions.
Excerpt from the Book
1 Introduction
Assurance companies face two main risk factors in the process of pricing annuity products namely the interest risk and the longevity risk. There are numerous products and possibilities for the insurers to hedge their interest risk using interest derivatives and long bonds. Hedging products against the longevity risk is uncommon but insurers have to take it into account when they are pricing their annuity products.
There are two types of longevity risks. On the one hand the idiosyncratic longevity risk and on the other hand the systematic longevity risk. With regards to the idiosyncratic longevity risk, individuals are faced with the issue that they need to invest in assets for their retirement in spite of an uncertain span of lifetime and thus an uncertain investment horizon. Pricing of life annuities could be done according to corresponding mortality tables. If the clients of an insurer die on average according to mortality rates provided by such tables, the revenues of the insurer should be sufficient to ensure the payments for the clients who are still alive. The issue out of a pension fund perspective is that longevity has been improving over time and clients could live longer than anticipated. These improvements occurred in an unpredictable way, especially at higher ages according to Cairns et al. (2006). Insurers therefore made false calculations of the insurance premium and suffered losses due to pensioners living longer than anticipated.
Summary of Chapters
1 Introduction: This chapter introduces the two primary risks for annuity providers, specifically focusing on the challenges posed by systematic longevity risk and the necessity of stochastic modeling.
2 Literature Review: This section covers the foundational Lee and Carter (1992) model and examines prior research on how systematic risk affects household consumption and annuity pricing strategies.
3 Model Implementation: This chapter details the technical application of the CBD model, including the estimation of stochastic factors A_1 and A_2, the simulation of mortality for 2030, and the subsequent pricing of pension annuities.
4 Conclusion: The final chapter synthesizes the findings, confirming that while mortality rates show a downward trend, stable modeling is crucial for providing affordable and sustainable annuity products in an aging society.
Keywords
Longevity risk, Pension fund, Systematic risk, Idiosyncratic risk, Mortality forecasting, CBD model, Lee-Carter model, Annuity pricing, Stochastic modeling, Human Mortality Database, Life expectancy, Demographic change, Interest risk, Survival probability, Immediate Pension Annuity Factor
Frequently Asked Questions
What is the core subject of this paper?
The paper examines the impact of longevity risk on pension funds and insurers, specifically how systematic improvements in life expectancy create financial risks that require sophisticated stochastic modeling to manage.
What are the central thematic fields addressed?
The central themes include mortality forecasting, the implementation of stochastic two-factor models (specifically the CBD model), and the financial application of these models to price lifetime annuities.
What is the primary goal or research question?
The goal is to estimate the CBD two-factor model using U.S. male mortality data to predict average mortality for 2030 and use those findings to calculate the fair price of immediate pension annuities.
Which scientific methodology is employed?
The author employs a quantitative approach using discrete-time series analysis and simulations in Matlab, including the use of ordinary least squares and Cholesky decomposition to process historical mortality data.
What topics are covered in the main body?
The main body focuses on the estimation and prediction of mortality factors A_1 and A_2, the calculation of mortality rates for 2030, and the derivation of annuity pricing based on various risk-free interest rates.
Which keywords best characterize this work?
The work is best characterized by terms such as longevity risk, CBD model, annuity pricing, systematic mortality changes, and stochastic forecasting.
Why are mortalities for people under the age of 20 excluded from the model?
Mortalities for younger individuals often contain extreme values that are not relevant for modeling the mortality patterns typically associated with retirement age, which is the focus of the annuity analysis.
How does the CBD model improve upon the original Lee-Carter model?
The CBD model utilizes two stochastic factors to capture the random element in the development of mortality rates, where one factor influences all ages equally and the second allows for age-dependent variations, resulting in a more dynamic model.
- Quote paper
- Lasse Erdweg (Author), 2015, Longevity Risk from a Pension Fund Perspective, Munich, GRIN Verlag, https://www.hausarbeiten.de/document/310639
