Author: AM Ngugi, F Maré and R Kufakunese

Abstract: The purpose of this study is to investigate the pricing of variable annuity embedded derivatives using
a suitably refined model for the underlying assets, in this case the Johannesburg Securities Exchange
FTSE/JSE All Share Index (ALSI). This is a practical issue that life insurers face worldwide in the
management of embedded derivatives. We consider the Variance-Gamma (VG) framework to model
the underlying data series. The VG process is useful in option pricing given its ability to model higher
moments, skewness and kurtosis and to capture observed market dynamics. The framework is able
to address the inadequacies of some deterministic pricing approaches used by life insurers, given the
increasing complexity of the option-like products sold.
Keywords: Embedded derivatives; options; variable annuity; Variance-Gamma; hedging