A Pricing Model of Airbag Options with Discrete Monitoring

Abstract

In this paper, we propose a pricing model of airbag options with discrete monitoring, time-varying barriers, early exercise opportunities, and other popular features simultaneously. We show that the option value is a viscosity solution of a PDE system. In particular, a closed-form solution is obtained in the classic Black-Scholes economy with no early exercise opportunities. For the general case, we develop a numerical algorithm and conduct an extensive numerical analysis after calibrating the model to the CSI 500 index in China. Greek letters, dynamic hedging, and assessment of investing in airbag options are also studied.