A0312
Title: Modeling and estimating asset price jumps using CARMA-Hawkes processes and high-frequency VIX data
Authors: Lorenzo Mercuri - University of Milan (Italy) [presenting]
Abstract: A self-exciting point process with a continuous-time autoregressive moving average intensity is introduced, referred to as the CARMA(p,q)-Hawkes model. This framework generalizes the classical Hawkes process by replacing the Ornstein Uhlenbeck intensity with a CARMA(p,q) process, where the associated state is driven by the counting process itself. While maintaining the analytical tractability of the Hawkes process, the proposed model captures more intricate temporal structures commonly observed in financial market data. Building on this foundation, a novel asset price model is developed based on a compound CARMA(p,q)-Hawkes process with random jump sizes. This construction can serve as a building block for pure-jump, stochastic volatility jump-diffusion (SVJ) and stochastic volatility model with jumps in the stock price and the volatility (SVJJ). A calibration approach is also proposed, formulated as a maximum likelihood estimation problem. A key challenge in this procedure is the filtering of the unobservable volatility and CARMA-driven intensity processes. While previous studies have relied on the extended Kalman filter or Bayesian filtering techniques, an alternative strategy is explored that recovers these latent processes directly from high-frequency VIX data. Finally, the performance of the estimation method is assessed through both simulation studies and empirical analysis using real data.
