EURO 2024 Copenhagen
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3996. Pricing Options with a Compound CARMA(p,q)-Hawkes model

Invited abstract in session TB-63: Risk Management and Cryptoassets, stream OR in Banking, Finance and Insurance: New Tools for Risk Management.

Tuesday, 10:30-12:00
Room: S14 (building: 101)

Authors (first author is the speaker)

1. Andrea Perchiazzo
Department of Economics, Management and Quantitative Methods, University of Milan
2. Lorenzo Mercuri
University of Milan
3. Edit Rroji
University of Milano-Bicocca

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 we propose a compound CARMA(p,q)-Hawkes model 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. We conduct an analysis to assess the effectiveness of this pricing model in replicating the volatility surface observed in market option data.

References:
Mercuri, L., Perchiazzo, A., & Rroji, E. (2024). A Hawkes model with CARMA (p, q) intensity. Insurance: Mathematics and Economics.

Keywords

Status: accepted

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