Valuation of GLWB–LTC Annuities with Lévy Equity Dynamics, Stochastic Interest Rates and Health-State Transitions

By Andrea Molent

Rating

1437
Battle Count: 76

Relevance

3/10
The paper is primarily focused on actuarial/insurance product pricing rather than trading strategies. However, the Lévy equity dynamics, jump risk modeling, and stochastic interest rate frameworks are relevant to quantitative finance more broadly. The PIDE solution techniques and Monte Carlo methods have transferable applications in derivatives pricing and risk management. The surrender boundary analysis touches on optimal stopping problems relevant to structured products.

Implementation Complexity

8/10
The hybrid tree-IMEX method requires: (1) constructing a recombining Hull-White trinomial tree with moment-matching probabilities, (2) implementing IMEX finite difference schemes for PIDEs with nonlocal jump operators, (3) handling multi-state health transitions with matrix exponentiation, (4) managing annual contract event sequences with bang-bang optimization, (5) similarity reduction for dimensionality, (6) proper boundary treatment including depleted-account state, and (7) interpolation on logarithmic grids. The combination of tree methods, PIDE solvers, multi-state models, and optimal stopping makes this highly complex.

Reproducibility

4/5
The paper provides detailed parameter tables (Tables 2-3), numerical configurations (Table 5), and algorithm pseudocode (Algorithm 1). MATLAB code is available from the author upon request. Health-transition matrices are based on Pritchard (2006) and Lévy parameters from Bacinello et al. (2016). All numerical results are reported with sufficient detail for replication.

About this paper

Methodology: Hybrid Tree-IMEX Method. Problem types: Pricing/Valuation, Risk Management, Optimization, Survival Analysis, Portfolio Optimization.

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