Valuation of GLWB annuities with optional conversion to combo products providing LTC benefits

To address the critical challenges faced by the elderly population in the field of long-term care, this paper proposes a novel insurance product that flexibly combines a variable annuity with a guaranteed lifelong withdrawal benefit (GLWB) rider and long-term care (LTC) insurance. Specifically, the proposed insurance product incorporates a conversion period during which the policyholder can flexibly decide whether to convert the standard annuity contract into a combo product that integrates LTC benefits. Using the Fourier cosine (COS) method combined with Markov chain approximation techniques, we develop a unified framework to price the GLWB annuity under general stochastic volatility models. By improving the algorithm through cubic spline interpolation, we achieve efficient valuation of this contract. The stochastic volatility models considered in this study include the Heston model, 3/2 model, 4/2 model, Hull-White model, and Scott model. The impact of annuity model parameters, conversion timing, and the policyholder's gender on the GLWB value is analyzed.