Introducing State Contingencies in Longevity Risk Models with n-State Stochastic Longevity Data Generating Process - Applications to Asset Pricing of Life-Contingent Claims and Decumulation Phase Asset Allocation

Russell Nel, PhD

Abstract :

Asset Pricing Of Life-Contingent Claims with n-State Stochastic Longevity Data Generating Process: Longevity risk is expected to dominate all major public and private sectors for the foreseeable future. The research hypothesizes that idiosyncratic impaired-health states, in the age cohort exceeding 65 years, is a crucial clinical variable required to profile individual life expectancy with subsequent valuation and risk management implications. Currently, the pension fund and insurance markets rely on life expectancy estimates derived from age-specific deterministic mortality tables that may be adjusted by at least two subjective medical reviews, however providing significant unacceptable variability. This research adopts a scientific approach, developing the mathematical framework for a n-State Longevity Data Generating Process (“DGP”) in order to derive conditional (age, impaired-health) life expectancy. Subsequently, utilizing the n-State Longevity DGP, a pricing framework for life-contingent claims (life settlements) is developed that is consistent with existing methods of valuation, risk management and sensitivity analysis widely used in fixed income products. The n-State Longevity DGP is modelled as a time-varying absorbing Markov process, used to describe impaired-health progression as a series of probable transitions between health states. Transition rate parameters are estimated with Bayesian MCMC using clinical dementia as the impaired-health data set, while transition probabilities are computed by numerically solving the Kolmogorov forward equations for a 7-State process. Key empirical results show that when impaired-health states are considered, asset valuations can differ by up to 27% and Sharpe ratio’s ranging between 0.49-1.12 versus benchmark assets Sharpe ratio range of between 0.21-0.72.

Decumulation Phase Asset Allocation with n -State Stochastic Longevity DGP: Life annuities, utilized to provide life-contingent income in the decumulation phase of the life-cycle, has experienced low market demand largely due to irreversibility, loss of bequest and asymmetric mortality beliefs and excludes impaired-health state risk. The research contemplates a health-state option (“HSO”) strategy and hypothesizes that monetizing latent health-state options, owned by life policy holders, in the secondary life settlement market increases Investor welfare gain. We posit a strategy in which the Investor, on the retirement date, will have liquid retirement assets and hold a portfolio of life policies. In the decumulation phase, Investors will be exposed to longevity risk, impaired-health state risk and capital market risk with allocation decisions to consumption, market portfolio choice and life annuities. In this setting, allocation decisions and welfare gain is modeled and simulated for the proposed HSO strategy versus benchmark allocation strategies, in a multidimensional state-space. Welfare gain, observed in the evolution of the system state-variables (wealth, bequest, consumption) utilize a n-State Longevity DGP with transition probabilities calibrated to clinical dementia (impaired-health state) data using Bayesian MCMC to estimate transition rate parameters. Heuristic market portfolios utilize the Farma/French 3-factor model while life annuity pricing is based on age-specific market observations. Longevity properties generated from n-State Longevity DGP provide critical allocation decision information and imply that observed life annuity pricing is overvalued with increasing impaired health-states. Empirical results and state-space simulations show that the proposed HSO strategy outperforms benchmark allocation strategies for all state-variables, allocation decisions, and heuristic portfolio choice. The proposed HSO (for the adjusted consumption state-variable and gradual annuitization) delivers monotonically increasing value with increasing Age [20% (Age 65) to 35 % (Age74)] and exponentially increasing value with increasing impaired-health states [at Age 65, HS-0 (20%) to HS-6(163%)]. The key results show significant improvement in utility of bequest when the HSO strategy is implemented, largely since the life policy portfolio is retained over the decumulation period. In the event of demise of the Investor, the utility of bequest is improved upon by the value of the net death benefit derived from the life policy.

Publication date of the thesis

Thesis committee

Supervisor: Lionel Martellini, EDHEC Business School

External reviewer:  Enrico Biffis, Imperial College London 

Other committee member: René Garcia, EDHEC Business School