35 research outputs found
Differential Sensitivity in Discontinuous Models
Differential sensitivity measures provide valuable tools for interpreting
complex computational models used in applications ranging from simulation to
algorithmic prediction. Taking the derivative of the model output in direction
of a model parameter can reveal input-output relations and the relative
importance of model parameters and input variables. Nonetheless, it is unclear
how such derivatives should be taken when the model function has
discontinuities and/or input variables are discrete. We present a general
framework for addressing such problems, considering derivatives of
quantile-based output risk measures, with respect to distortions to random
input variables (risk factors), which impact the model output through
step-functions. We prove that, subject to weak technical conditions, the
derivatives are well-defined and derive the corresponding formulas. We apply
our results to the sensitivity analysis of compound risk models and to a
numerical study of reinsurance credit risk in a multi-line insurance portfolio
A Dynamic Programming Algorithm for the Valuation of Guaranteed Minimum Withdrawal Benefits in Variable Annuities
In this paper we present a dynamic programming algorithm for pricing variable annuities
with Guaranteed Minimum Withdrawal Benefits (GMWB) under a general LĂ©vy processes
framework. The GMWB gives the policyholder the right to make periodical withdrawals
from her policy account even when the value of this account is exhausted. Typically, the
total amount guaranteed for withdrawals coincides with her initial investment, providing
then a protection against downside market risk. At each withdrawal date, the policyholder
has to decide whether, and how much, to withdraw, or to surrender the contract. We
show how different levels of rationality in the policyholder’s withdrawal behaviour can be modelled. We perform a sensitivity analysis comparing the numerical results obtained for
different contractual and market parameters, policyholder behaviours, and different types
of LĂ©vy processes
Longevity Basis Risk A methodology for assessing basis risk
This technical report details the methodology developed on behalf of the LBRWG to assess longevity basis risk. A user-guide which provides a high level summary of this report has also been produced. Together these documents form the key outputs of the first phase of a longevity basis risk project
commissioned and funded by the IFoA and the LLMA, and undertaken on our behalf by Cass Business School and Hymans Robertson LLP
Forecasting mortality in subpopulations using Lee-Carter type models: A comparison
The relative performance of multipopulation stochastic mortality models is investigated. When targeting mortality rates, we consider five extensions of the well known Lee–Carter single population extrapolative approach. As an alternative, we consider similar structures when mortality improvement rates are targeted. We use a dataset of deaths and exposures of Italian regions for the years 1974–2008 to conduct a comparison of the models, running a battery of tests to assess the relative goodness of fit and forecasting capability of different approaches. Results show that the preferable models are those striking a balance between complexity and flexibility
A comparative study of two population models for the assessment of basis risk in longevity hedges
Longevity swaps have been one of the major success stories of pension scheme derisking in recent years. However, with some few exceptions, all of the transactions to date have been bespoke longevity swaps based upon the mortality experience of a portfolio of named lives. In order for this market to start to meet its true potential, solutions will ultimately be needed that provide protection for all types of members, are cost effective for large and smaller schemes, are tradable, and enable access to the wider capital markets. Index-based solutions have the potential to meet this need; however concerns remain with these solutions. In particular, the basis risk emerging from the potential mismatch between the underlying forces of mortality for the index reference portfolio and the pension fund/annuity book being hedged is the principal issue that has, to date, prevented many schemes progressing their consideration of index-based solutions. Two-population stochastic mortality models offer an alternative to overcome this obstacle as they allow market participants to compare and project the mortality experience for the reference and target populations and thus assess the amount of demographic basis risk involved in an index-based longevity hedge. In this paper, we systematically assess the suitability of several multi-population stochastic mortality models for assessing basis risks and provide guidelines on how to use these models in practical situations paying particular attention to the data requirements for the appropriate calibration and forecasting of such models