The rough Hawkes Heston stochastic volatility model
研究了一个结合粗糙波动率和跳跃聚集现象的赫斯顿随机波动率模型扩展，该模型能精确捕捉标普500和VIX期权的隐含波动率微笑行为。
Abstract We study an extension of the Heston stochastic volatility model that incorporates rough volatility and jump clustering phenomena. In our model, named the rough Hawkes Heston stochastic volatility model, the spot variance is a rough Hawkes‐type process proportional to the intensity process of the jump component appearing in the dynamics of the spot variance itself and the log returns. The model belongs to the class of affine Volterra models. In particular, the Fourier‐Laplace transform of the log returns and the square of the volatility index can be computed explicitly in terms of solutions of deterministic Riccati‐Volterra equations, which can be efficiently approximated using a multi‐factor approximation technique. We calibrate a parsimonious specification of our model characterized by a power kernel and an exponential law for the jumps. We show that our parsimonious setup is able to simultaneously capture, with a high precision, the behavior of the implied volatility smile for both S&P 500 and VIX options. In particular, we observe that in our setting the usual shift in the implied volatility of VIX options is explained by a very low value of the power in the kernel. Our findings demonstrate the relevance, under an affine framework, of rough volatility and self‐exciting jumps in order to capture the joint evolution of the S&P 500 and VIX.