European option pricing under stochastic volatility jump-diffusion models with transaction cost. (1st May 2020)

• Record Type: Journal Article
• Authors: Tian, Yingxu; Zhang, Haoyan
• Is Part Of: Computers & mathematics with applications. Volume 79:issue 9(2020)
• Page Start: 2722
• Page End: 2741
• Publication Date: 2020-05-01
• Subjects: Option pricing -- Stochastic volatility -- Jump diffusion -- Transaction costs -- Nonlinear PIDE -- Positions readjustment; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2019.12.001
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: In this paper, we consider an underlying general stochastic volatility jump-diffusion model. Option pricing under this general model with transaction costs will lead to handling with nonlinear partial integro-differential equations (here after PIDE). In this case, option replication in a discrete-time framework with transaction costs and the non-uniqueness option pricing in such incomplete market will be studied. Observing and introducing a traded proxy for the volatility in the modern market, we acquire a nonlinear PIDE in the advent of transaction costs. Under appropriate regularity conditions, the existence of the strong solution to this pricing problem has been proved. The corresponding self-financing and positions readjustment for pricing a portfolio will also be discussed in the end.