PhD Thesis Proposal - Public Lecture - Yixing Zhao

Title: Valuation and risk management of longevity products with investment guarantees

Abstract:

Over the past decades, numerous insurance products whose values are linked to risky assets, have emerged rapidly. This type of products has option-embedded features and typically involves at least two risk factors: interest and mortality rates. The need for models to describe the behaviour of these risk factors accurately is paramount for insurance companies. This thesis proposal puts forward approaches in dealing with dependent risk factors and how such dependence impacts the pricing and hedging of longevity products with option-embedded characteristics. Various methods will be developed to facilitate the computation of prices and risk measures of longevity products with investment guarantees.

This research consists of six related projects, the first two of which were already completed. We briefly described these projects as follows: (i) A pricing framework is developed for a guaranteed annuity option (GAO) assuming stochastic and correlated interest and mortality rates. The short-rate process and force of mortality are governed by the Cox-Ingersoll-Ross (CIR) and Lee-Carter (LC) models, respectively. The change of measure technique in conjunction with the concept of comonotonicity was utilised in GAO-prices calculation. (ii) Extending beyond interest and risk factors, we constructed a two-decrement model for the valuation and risk measurement of GAO. Interest rate, mortality and lapse risk are assumed dependent and modelled as affine-diffusion processes. Risk measures were obtained via the moment-based density method. (iii) We shall consider the framework described in (i) by adopting the two-factor Hull-White model for the short-rate process with a view towards attaining certain efficient pricing representations. (iv) A regime-switching approach will be formulated for the valuation of guaranteed minimum maturity benefits (GMMBs).  But, more specifically in this case, the hidden Markov model (HMM) will be used to describe the evolution of risk processes and HMM filtering technique will be employed to generate model parameter estimates. (v) Valuation and risk management of a guaranteed minimum death benefit (GMDB) will be explored. The stock index, interest rate and mortality are driven by hidden Markov chains. Some well-known risk measures as well as the total gross calculated requirement provided by Life Insurance Capital Adequacy Test (LICAT) will be determined via the Monte-Carlo simulation method. (vi) We will extend the results in projects (iv) and (v) and apply them in the valuation of a guaranteed minimum accumulation benefit (GMAB). Sensitivity Analysis will be performed to study the impacts of risk factors on the prices and risk measures.

Results from the first 2 projects will be presented. This research work is supervised by Dr. Rogemar Mamon.

Supervisor: Dr. Rogemar Mamon