Abstract
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.
Highlights
Over the years, many practical and academic contributions have been offered describing Variable Annuities (VAs) and their embedded guarantees.Variable annuities (VAs) are life insurance products with investment guarantees providing substantial investment guarantees along with tax privileges and prudently managed assets
We are interested in the expected value and the conditional value at risk at a chosen confidence level of 95% of the portfolio at inception, for a static hedging strategy (Section 4.2)
This paper studies, from the insurer point of view, a VA product offering Guaranteed Minimum Death Benefits (GMDBs) and Guaranteed Minimum Maturity Benefits (GMMBs) guarantees
Summary
Many practical and academic contributions have been offered describing VAs and their embedded guarantees. The resulting economic impact to the insurer selling the guarantee is based on how the future real world scenario plays out Given these considerations, it may be useful for an insurer to assess real world risk associated with embedded guarantees of its VA portfolio, once pricing is done and a risk management strategy is adopted. It is assumed that the insurer is able to implement a static hedge This allows us to compare the impact of the two multivariate processes used to model the rate of return of the basket of assets on the value of the portfolio. Variable annuities are written on more than one asset, in practice, single asset univariate stochastic investment models are mostly used for pricing and hedging purposes This may lead to problems such as basis risk or a lack of flexibility with respect to asset allocations [6].
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