Can I read Pricing VIX options under the Heston-Hawkes stochastic volatility model on EtoBox?

Pricing VIX options under the Heston-Hawkes stochastic volatility model by Font, Oriol Zamora is a scholarly article available to read on EtoBox.

What is Pricing VIX options under the Heston-Hawkes stochastic volatility model about?

We derive a semi-analytical pricing formula for European VIX call options under the Heston-Hawkes stochastic volatility model introduced in arXiv:2210.15343. This arbitrage-free model incorporates the volatility clustering feature by adding an independent compound Hawkes process to the Heston volatility. Using the Markov property of the exponential Hawkes an explicit expression of $\text{VIX}^2$ is derived as a linear combination of the variance and the Hawkes intensity. We apply qualitative ODE theory to study the existence of some generalized Riccati ODEs. Thereafter, we compute the joint characteristic function of the variance and the Hawkes intensity exploiting the exponential affine structure of the model. Finally, the pricing formula is obtained by applying standard Fourier techniques.

Author

Font, Oriol Zamora

Published

2024

Language

EN