Dupret Jean-Loup, Barbarin Jérôme, Hainaut Donatien
LIDAM, Institute of Statistics, Biostatistics and Actuarial Sciences, Université Catholique de Louvain, Louvain-La-Neuve, Belgium.
Eur Actuar J. 2023;13(1):235-275. doi: 10.1007/s13385-022-00317-1. Epub 2022 Jun 25.
The Rough Fractional Stochastic Volatility (RFSV) model of Gatheral et al. (Quant Financ 18(6):933-949, 2014) is remarkably consistent with financial time series of past volatility 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. (Quant Financ 16(6):887-904, 2016) and the rough Heston model of El Euch et al. (Risk 84-89, 2019). We now show practically how to expand these two rough volatility models at larger time scales, we analyze their implications for the pricing of long-term life insurance contracts and we explain why they provide a more accurate fair value of such long-term contacts. In particular, we highlight and study the long-term properties of these two rough volatility models and compare them with standard stochastic volatility models such as the Heston and Bates models. For the rough Heston, we manage to build a highly consistent calibration and pricing methodology based on a stable regime for the volatility at large maturity. This ensures a reasonable behavior of the model in the long run. Concerning the rBergomi, we show that this model does not exhibit a realistic long-term volatility with extremely large swings at large time scales. 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.
加瑟尔等人（《定量金融》，2014年第18卷第6期，第933 - 949页）提出的粗糙分数阶随机波动率（RFSV）模型与过去波动率数据的金融时间序列以及观察到的隐含波动率曲面显著一致。从RFSV模型推导出了两种易于处理的实现方式，分别是拜尔等人（《定量金融》，2016年第16卷第6期，第887 - 904页）的rBergomi模型和埃尔·尤赫等人（《风险》，2019年，第84 - 89页）的粗糙赫斯顿模型。我们现在实际展示如何在更大的时间尺度上扩展这两个粗糙波动率模型，分析它们对长期人寿保险合同定价的影响，并解释它们为何能为此类长期合同提供更准确的公允价值。特别是，我们突出并研究这两个粗糙波动率模型的长期特性，并将它们与标准随机波动率模型（如赫斯顿模型和贝茨模型）进行比较。对于粗糙赫斯顿模型，我们基于大期限波动率的稳定状态构建了一种高度一致的校准和定价方法。这确保了模型在长期内具有合理的表现。关于rBergomi模型，我们表明该模型在大时间尺度上不会呈现出具有极大波动的现实长期波动率。我们还表明，与高度易于处理的粗糙赫斯顿模型不同，rBergomi模型在校准方面不够快。与标准随机波动率模型相比，粗糙赫斯顿模型因此能够高效地为嵌入路径依赖期权的长期人寿保险合同提供更准确的公允价值，同时与历史数据和风险中性数据高度一致。
