Pricing discrete barrier options under jump-diffusion model with liquidity risk

Abstract

Classical option pricing theories are usually built on the paradigm of competitive and frictionless markets, while ignoring the impact of market liquidity on underlying asset prices. In this paper, the importance of liquidity risk on discrete barrier option pricing is analyzed. First, we propose a new model for describing the asset price dynamics in the presence of jumps and liquidity risks, which is able to capture empirically observed patterns. Based on the COS method, we then derive the analytical approximation formulas for the prices of the discrete barrier options. Numerical experiments demonstrate the accuracy of our proposed pricing model by comparing the analytical approximation solutions with Monte Carlo simulation. Finally, empirically studies are carried out to show the superiority of our model based on SSE 50 ETF options. The numerical and empirical results support our idea of introducing liquidity risk and jumps into the underlying asset price dynamics.