Impact of rough stochastic volatility models on long-term life insurance pricing

The Rough Fractional Stochastic Volatility (RFSV) model of Gatheral et al. [18] is remarkably consistent with financial time series data as well as with the observed implied volatility surface. Two tractable implementations are derived from the RFSV with the rBergomi model of Bayer et al. [3] and the rough Heston model of El Euch et al. [13]. We now show practically how to calibrate these two rough-type models and how they can price long-term equity-linked life insurance claims. This way, we analyze more closely their longterm properties and compare them with standard stochastic volatility models such as the Heston and Bates model. For the rough Heston, we build a highly consistent calibration and pricing methodology based on a long-term stationary regime for the volatility. This ensures a reasonable behavior of the model in the long run. Concerning the rBergomi, it does not admit a stationary volatility process and hence, this model does not exhibit realistic volatility paths for large maturities. We also show that this rBergomi is not fast enough for calibration purposes, unlike the rough Heston which is highly tractable. Compared to standard stochastic volatility models, the rough Heston hence provides efficiently a more accurate fair value of long-term life insurance contracts embedding path-dependent options while being highly consistent with historical and risk-neutral data.