Modelling the Fair Value of Annuities Contracts: The Impact of Interest Rate Risk and Mortality Risk

22 Pages Posted: 11 Jun 2007

See all articles by Laura Ballotta

Laura Ballotta

Sir John Cass Business School - City, University of London

Giorgia Esposito

University of Rome I - Department of Actuarial and Financial Sciences

Steven Haberman

City University London - Faculty of Actuarial Science

Date Written: December 2006

Abstract

The purpose of this paper is to analyze the problem of the fair valuation of annuities contracts. The market consistent valuation of these products requires a pricing framework which includes the two main sources of risk affecting the value of the annuity, i.e. interest rate risk and mortality risk. As the IASB has not set any specific guidelines as to which models are the most appropriate for these risks, in this note we consider a range of different models calibrated with historical data. We calculate the fair value of the annuity as a portfolio of zero coupon bonds, each with maturity set equal to the date of the annuity payments; the weights in the portfolio are given by the survival probabilities. Moreover, we focus on the additional information provided by stochastic simulations in order to define a suitable risk margin. The nature of the risk margin is one of the main key issues concerning the IASB and Solvency project.

Keywords: annuity contracts, fair value, market value margin, stochastic mortality

JEL Classification: G22, M41, M44, M47

Suggested Citation

Ballotta, Laura and Esposito, Giorgia and Haberman, Steven, Modelling the Fair Value of Annuities Contracts: The Impact of Interest Rate Risk and Mortality Risk (December 2006). Available at SSRN: https://ssrn.com/abstract=992211 or http://dx.doi.org/10.2139/ssrn.992211

Laura Ballotta

Sir John Cass Business School - City, University of London ( email )

Faculty of Finance
106 Bunhill Row
London, EC1Y 8TZ
United Kingdom

HOME PAGE: http://www.city.ac.uk/people/academics/laura-ballotta

Giorgia Esposito (Contact Author)

University of Rome I - Department of Actuarial and Financial Sciences ( email )

Piazzale Aldo Moro 5
Roma, Rome 00185
Italy

Steven Haberman

City University London - Faculty of Actuarial Science ( email )

London
United Kingdom

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