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

Abstract

In this paper, the pricing of financial derivatives and the calculation of their delta Greek are investigated as 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. Due to the dependence of asset price on the information of the intensity process, conditional expectation attribute to show boundedness of moments of Malliavin weights and the underlying asset is essential. Our approach is validated through numerical experiments, highlighting its effectiveness and potential for risk management and hedging strategies in markets characterized by jump and stochastic intensity dynamics.