European option pricing under stochastic volatility jump-diffusion models with transaction cost

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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.