Pricing inflation-linked variable annuities under stochastic interest rates

Equities have long been dubbed the natural hedge against inflation. However, empirical findings have implied just the opposite, that there exists a negative correlation between stock returns and inflation. The rising inflation and slowing economic growth that we are experiencing in today’s market environment pose an even greater threat to the general investors, especially on their retirement planning. In this paper, we present various inflation-linked variable annuities which are designed to help investors protect their portfolios from inflation risk. Assuming a Gaussian HJM framework for the nominal and real term structures, closed-form pricing formulas are obtained for these inflation-linked annuity products.