Ayub Ahmadi | Searcharxiv

arXiv2025

Hedging of exotic options in Hawkes jump-diffusion models by Malliavin calculus

In financial mathematics, the calculation of the Greeks, especially the delta, is emphasized due to its role in risk management. In this article, we employ Malliavin calculus to determine the delta of European and Asian options, where the underlying asset evolves according to a Hawkes jump-diffusion process. A central feature is that the Hawkes jump intensity is stochastic, which substantially affects the delta representation.

math.PR↗

arXiv2025

Pricing and delta computation in jump-diffusion models with stochastic intensity by Malliavin calculus

This paper investigates the pricing of financial derivatives and the calculation of their delta Greek when the underlying asset is a jump-diffusion process in which the stochastic intensity component follows the CIR process. Utilizing Malliavin derivatives for pricing financial derivatives and challenging to find the Malliavin weight for accurately calculating delta will be established in such models. Because asset prices rely on information from the intensity process, the moments of the Malliavin weights and the underlying asset must be bound. We apply the Euler scheme to show the convergence of the approximated solution, a financial derivative, and its delta Greeks and we have established the convergence analysis. Our approach has been validated through numerical experiments, highlighting its effectiveness and potential for risk management and hedging strategies in markets characterized by jump and stochastic intensity dynamics.

q-fin.PR↗