Valuation and Risk Assessment of a Portfolio of Variable Annuities: A Vector Autoregression Approach

This paper focuses on assessing the financial position of an insurer issuing a portfolio of Variable Annuities (VAs). Two multivariate models for the underlying and the interest rate are considered. The first model uses a single total rate of return for the basket of assets. The second one, jointly models the rates of return on the n assets in the basket. For simplicity, the insurer is assumed to be able to implement a static hedging programme to manage the risk. As an example, a homogeneous portfolio of VAs with GMDB and GMMB guarantees offering different investment opportunities to the policyholders is studied. The insurer can choose to rebalance the basket of assets regularly or not. Results for these two cases are presented.