A Mixed Bond and Equity Fund Model for the Valuation of Variable Annuities

Variable annuity policies are typically issued on mutual funds invested in both fixed income and equity asset classes. However, due to the lack of specialized models to represent the dynamics of fixed income fund returns, the literature has primarily focused on studying long-term investment guarantees on single-asset equity funds. This article develops a mixed bond and equity fund model in which the fund return is linked to movements of the yield curve. Theoretical motivation for our proposed specification is provided through an analogy with a portfolio of rolling horizon bonds. Moreover, basis risk between the portfolio return and its risk drivers is naturally incorporated into our framework. Numerical results show that the fit of our model to Canadian variable annuity data is adequate. Finally, the valuation of variable annuities is illustrated and it is found that the prevailing interest rate environment can have a substantial impact on guarantee costs