Valuation of variable annuities under the Volterra mortality and rough Heston models

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The paper is primarily focused on actuarial/insurance product valuation rather than trading strategies. However, the rough Heston model and path-signature methods have relevance to derivatives pricing and risk management in quantitative finance. The optimal stopping framework is analogous to American option pricing, which is relevant to trading. The computational techniques (deep signature LSMC) could be adapted for path-dependent option pricing in trading contexts.

The implementation requires: (1) rough path theory and signature computation (iisignature library), (2) fast algorithm for rough Heston simulation with exponential kernel approximation, (3) Volterra integral equation discretization with fractional kernels, (4) neural network training at each time step in backward induction, (5) Monte Carlo simulation of joint equity-mortality paths, (6) bisection for fair fee, (7) two-pass procedure for look-ahead bias removal. The mathematical sophistication (rough path theory, SVIEs, Riccati-Volterra equations) and computational demands (3.5 hours per fee computation) make this highly complex.

The paper provides detailed model specifications, calibrated parameters (Tables 1-3), hyperparameter choices (Table 2), and algorithmic steps. However, no code repository is mentioned. The use of the iisignature library and specific calibration data (Human Mortality Database, US males born 1920) are referenced. The rough Heston parameters are taken from Jeng and Kilicman (2021). Reproduction would require implementing the fast algorithm for rough Heston simulation, the Volterra mortality Euler scheme, signature computation, and the deep LSMC backward induction.