Abstract:
It is well known that interest rate risk is a dominating factor when pricing long-dated contingent claims.
The Heston stochastic volatility model fails to capture this risk as the model assumes a constant interest
rate throughout the life of the claim. To overcome this, the risk-free interest rate can be modelled by a
Hull-White short rate process and can be combined with the Heston stochastic volatility model to form
the so-called Heston-Hull-White model. The Heston-Hull-White model allows for correlation between
the equity and interest rate processes, a component that is important when pricing long-dated contingent
claims. In this paper, we apply the Heston-Hull-White model to price Guaranteed Minimum Maturity
Benefits (GMMBs) and Guaranteed Minimum Death Benefits (GMDBs) offered in the life insurance
industry in South Africa. We propose a further extension by including stochastic mortality rates based
on either a continuous-time Cox-Ingersoll-Ross short rate process or a discrete-time AR(1)-ARCH(1)
model. Our findings suggest that stochastic interest rates are the dominating factor when reserving for
GMMB and GMDB products. Furthermore, a delta-hedging strategy can help reduce the variability of
embedded derivative liabilities.
