|Institution:||University of New South Wales|
|Keywords:||Variable annuities; Longevity risk managment; Benchmark approach; Longevity derivatives; Long dated bonds|
|Full text PDF:||http://handle.unsw.edu.au/1959.4/54110|
Population ageing has presented new challenges and opportunities for insurance companies to address the increasing demand of products that are designed for the purpose of financing retirement. A change of pricing, modelling and risk management approach is required for insurers that are engaged in offering long term policies for retirement. This thesis addresses several pricing and risk management problems of long dated contracts from a supplier's perspective. The thesis begins with a study of market-based longevity risk management for a hypothetical life annuity portfolio subjected to longevity risk. Prices of longevity swaps and caps are derived analytically under a tractable Gaussian mortality model. Various hedging features exhibited by an index-based longevity swap and a cap are demonstrated with respect to different assumptions on the market price of longevity risk, the term to maturity of the hedging instruments and the size of the underlying annuity portfolio. Pricing and risk analysis of guaranteed lifetime withdrawal benefits embedded in variable annuities is studied next, with a focus on the interaction of equity and longevity risk. The guarantee is designed to protect policyholders from longevity risk and downside investment risk. It is priced using two approaches that are proved to be equivalent. Financial and longevity risks underlying the guarantee are quantified based on sensitivity and profit & loss analysis. Effectiveness of a static hedge of longevity risk is examined with respect to different levels of equity exposure. The benchmark approach, where the growth optimal portfolio is employed as the numeraire together with the real world probability measure as the pricing measure, is applied to investigate the pricing and hedging of long dated bonds. The thesis employs a tractable index model with stochastic interest rate to model the growth optimal portfolio. Non-parametric kernel-based technique is applied for parameter estimation. Closed-form expressions for bond prices and hedge ratios are derived under the real world probability measure. The thesis compares market prices of long dated bonds with model prices derived under the benchmark approach. A dynamic hedging strategy of long dated bonds is tested using empirical data.