A0399
Title: Pricing options with a compound CARMA(p,q)-Hawkes model
Authors: Andrea Perchiazzo - University of Milan (Italy) [presenting]
Lorenzo Mercuri - University of Milan (Italy)
Edit Rroji - Universita' degli studi di Milano-Bicocca (Italy)
Abstract: Recently, a novel self-exciting point process has been introduced in the literature, featuring a continuous-time autoregressive moving average intensity process. Such a model, named CARMA(p,q)-Hawkes, extends the traditional Hawkes process by integrating a CARMA(p,q) framework instead of an Ornstein-Uhlenbeck intensity. As a matter of fact, the proposed model maintains the same level of mathematical tractability as the Hawkes process (e.g., infinitesimal generator, backward and forward Kolmogorov equations, joint characteristic function), but it shows enhanced capability in reproducing complex time-dependent structures evident in several market data. Based on this framework, a compound CARMA(p,q)-Hawkes model is proposed, incorporating a random jump size independent of both the counting and intensity processes, which serves as a key component for a new option pricing model. An analysis is conducted to assess the effectiveness of this pricing model in replicating the volatility surface observed in market option data.
