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

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

Valuation of Variable Annuities Under Advanced Models Reveals New Insights for Swiss Insurers

Section 1 – What happened?

Swiss insurers and researchers have made a breakthrough in valuing variable annuity contracts with early surrender options under non-traditional models. A recent study published in an industry journal investigated the valuation of variable annuity contracts that offer guaranteed minimum maturity and death benefits to protect against market downturns. The researchers developed a novel deep signature Least Squares Monte Carlo approach to learn optimal surrender strategies on a discretized time grid, which can handle non-Markovian processes. The study found that the fair fee for these contracts increases with the Hurst parameters of both the stock volatility and the force of mortality.

Section 2 – Background & Context

Variable annuity contracts have become increasingly popular among Swiss retirees seeking guaranteed income and protection against market volatility. However, valuing these contracts under non-traditional models has proven to be a challenging task. Traditional numerical methods are often infeasible due to the optimal stopping problem introduced by the early surrender feature. The study's focus on non-Markovian processes, such as the rough Heston model for equity index and the Volterra-type stochastic model for force of mortality, reflects the growing need for more sophisticated models in the Swiss insurance industry.

Section 3 – Impact on Swiss SMEs & Finance

The study's findings have significant implications for Swiss insurers, who need to accurately value variable annuity contracts to ensure fair pricing and profitability. The increase in fair fees with the Hurst parameters of both the stock volatility and the force of mortality suggests that insurers should consider these factors when designing their variable annuity products. This may lead to more competitive pricing and better risk management for insurers, ultimately benefiting Swiss SMEs and investors seeking stable returns.

Section 4 – What to Watch

As the study's results are further developed and applied to real-world scenarios, Swiss insurers and regulators should monitor the impact on the industry. The adoption of non-traditional models and advanced numerical methods may lead to more accurate valuations and better risk management, but it also raises questions about the complexity and transparency of these models. Readers should watch for future developments in this area, including potential regulatory responses and industry-wide adoption of these new valuation methods.

Source

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

Published: April 1, 2026

Author: Wenyuan Li

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Disclaimer: This article is for informational purposes only and does not constitute financial advice. Consult a licensed financial advisor before making investment decisions.