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

TL;DR

This paper develops a Malliavin calculus-based method for pricing and delta computation of derivatives in jump-diffusion models with stochastic intensity, validated through convergence analysis and numerical experiments.

Contribution

It introduces a novel Malliavin calculus approach for derivative pricing and delta calculation in jump-diffusion models with stochastic intensity, including convergence proofs.

Findings

Convergence of Euler scheme for derivative prices and deltas.

Effective numerical validation of the proposed method.

Potential applications in risk management and hedging strategies.

Abstract

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.