Guaranteed annuity conversion options and their valuation * Laura Ballotta and Steven Haberman Faculty of Actuarial Science and Statistics, Cass Business School, City University London 106 Bunhill Row, EC1Y 8TZ E-mail address: L.Ballotta@city.ac.uk, S.Haberman@city.ac.uk Abstract In this chapter, we consider a theoretical model for the pricing and valuation of guaranteed annuity conversion options associated with certain unit-linked pension contracts in the UK. The valuation ap- proach is based on the similarity between the payoff structure of the contract and a call option written on a coupon-bearing bond. The model makes use of a one-factor Heath-Jarrow-Morton framework for the term structure of interest rates, in order to obtain a closed-form analytical solution to the fair valuation of the liabilities implied by these contracts. Mortality risk is incorporated via a stochastic model for the evolution over time of the underlying hazard rates. Numerical results are investigated and the sensitivity of the price of the option to changes in the key financial and mortality parameters is also analyzed. Keywords: guaranteed annuity option; hazard rates; reduction factor; longevity risk; risk neutral valuation; Heath-Jarrow-Morton model. * The financial support from the Society of Actuaries Committee on Knowledge Extension Research and the Actuarial Education on Research Fund is gratefully acknowledged. The authors would like to thank Prof. Gerald Rickayzen for his assistance with various C++ implementations. Earlier versions of this work have been presented at the 8 th International Vilnius Conference on Probability Theory and Mathematical Statistics, 6 th International Congress on Insurance: Mathe- matics and Economics (Cemapre, Lisbon), 37 th Society of Actuaries Actuarial Research Conference (Waterloo), 2 nd Conference in Actuarial Science & Finance (Samos). The authors would like to thank the participants of these conference and in particular the following: Phelim Boyle, Andrew Cairns, Moshe Milevsky, Anton Pelsser. 1