Centre of Financial Mathematics (CFM) Seminar Series

Speaker

Dr. Jonathan Ziveyi (School of Risk and Actuarial Studies, UNSW Business School)

Title

Pricing and Hedging of Guaranteed Minimum Benefits using Power Series Approximation Techniques

Abstract

Majority of the developed economies have off late been experiencing population ageing as people are living longer due to advances in medicines and lifestyle quality. Such developments have been putting a lot of pressure on governments, pension fund and annuity providers who are exposed to the resulting longevity risk. Variable annuities (VAs) constitute a class of financial products designed to tackle challenges associated with both investment and longevity risk. These contracts enable policyholders to participate in financial markets via linked investment funds and at the same time providing protection against long-term life contingencies. In this paper, we devise a numerical technique for pricing Guaranteed Minimum Benefit (GMB) riders embedded in variable annuity contracts. The method utilises multidimensional transforms of the characteristic function for the underlying stochastic processes and enables to express solutions of the associated pricing partial differential equations in terms of power series whose coefficients are derived and expressed in closed-form. Our results demonstrate the high computational efficiency of the series approximation method for the computation of prices and hedge ratios of GMBs under the stochastic volatility and stochastic interest rate modelling framework. The findings of the paper can help insurers with efficient quantification of various risks associated with GMB riders in variable annuities.