Pricing VIX options under the Heston-Hawkes stochastic volatility model

Autor:	Font, Oriol Zamora
Rok vydání:	2024
Předmět:	Quantitative Finance - Mathematical Finance 60G55 60H10 91G15 91G20
Druh dokumentu:	Working Paper
Popis:	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. Comment: 28 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2406.13508 Zobrazit plný text záznamu View this record from Arxiv