Market-consistent valuation and risk management of guaranteed annuity options

Abstract

The aim of the research is to develop a method and tools that facilitate the market-consistent valuation of a hypothetical portfolio of guaranteed-annuity options (GAOs). The fund underlying the GAOs carries a guaranteed minimum rate of return. This is accomplished by the construction of a stochastic economic-scenario generator. As an illustration, this scenario generator is calibrated to the South African market conditions as at the end of December 2007, although the same principles can be applied to all markets. The proposed model uses a one-factor Black-Karasinski interest-rate model and a Black-Scholes equity model. Further to this, a suitable hedge for this GAO portfolio against the main market risks (interest rates and equity returns) is sought. This research aims to evaluate a series of potential hedges and investigates the advantages and disadvantages of each. The sensivity of the GAO portfolio to improvements in future mortality is also investigated.