Pricing European options under a diffusion model with psychological barriers and leverage effect

摘要

This paper derives closed-form formulae for European options under a diffusion model when there exist psychological barriers and leverage effect in underlying dynamics. The state space of the proposed model is divided into different subregions by psychological barriers, and in each subregion, the model behaves like a constant elasticity of variance process. Within this framework, we derive both Laplace transform- and spectral expansion-based analytical solutions, which allow fast and accurate calculation of option prices. Numerical results are presented to explore the nontrivial properties of our model.