A General Framework for Modelling Mortality to Better Estimate Its Relationship with Interest Rate Risks

Abstract

The need for having a good knowledge of the degree of dependence between various risks is fundamental for understanding their real impacts and consequences, since dependence reduces the possibility to diversify the risks. This paper expands in a more theoretical approach the methodology developed in [6] for

Optimal Withdrawal Strategies in GLWB Variable Annuities

“…Although this model is very simple (it collapses to the well-known deterministic Gompertz force of mortality when α = σ µ = 0), it has the desirable property of producing strictly positive paths with probability 1, provided that 2α > σ 2 µ . Moreover, it allows to get a closed-form formula for the survival probability given in (7) (see, e.g., Fung et al (2014) and Dacorogna and Apicella (2016)). Hence we have…”

“…Following the same approach, our aim is to construct a dynamic programming algorithm for pricing variable annuities with GLWB under a stochastic mortality framework that allows to capture systematic longevity improvements as well as mortality shocks due, e.g., to pandemics. Although our set-up is very general and only requires the Markovian property for the mortality intensity and the asset price processes, in the numerical implementation of the algorithm we model the former as an affine diffusion, namely a non mean reverting square root process (see e.g., Fung et al (2014) and Dacorogna and Apicella (2016)), and the latter, like in Bacinello et al (2016), as an exponential Lévy process. In this way we get a tractable and flexible stochastic model for efficient pricing and risk management of the GLWB.…”

Risk management of guaranteed minimum maturity benefits under stochastic mortality and regime-switching by Fourier space time-stepping framework

“…We assume that the policyholder retires at 60, the time to maturity is 10 years. We set t = 0 to represent the calendar year 2017 and assume that the individual's age is 50 + t at time t. The calibration procedure is inspired by Dacorogna and Apicella [10] which is to estimate the parameters based on minimizing of the Squared Error (Ψ) between stochastic mortality models and observed survival function. The parameters for OU model and FEL model are reported in Tabel 1 and parameters for Blackburn and Sherris two-factor model are reported in Tabel 2.…”

General Price Bounds for Guaranteed Annuity Options

“…In the context of the real world, a study by [7] to understand the relation between these two underlying risks demonstrates that the decline of interest rate in pre-industrial England was perhaps triggered by the decline of adult mortality at the end of the 17th century. More recently [8] examine correlation between mortality and market risks in periods of extremes such as a severe pandemic outbreak while [9] explore existence of this dependence within the Feller process framework. As remarked in the beginning of this section 'The Life Expectancy Revolution' has pressurised social security programmes of various nations thereby triggering fiscal crisis for governments who find it hard to fulfill the needs of an ever growing aging population.…”