On Continuity Correction for First-Passage Times in Jump Diffusion Models
傅承德中央大學統研所 上午 10:00–11:30 鴻經館 107 室摘要：
This paper studies first passage times of crossing a flat boundary under mixed exponential jump diffusion models. We establish a continuity correction for the joint distribution of a first passage time and its stopped underlying process when the event of crossing is monitored only discretely. The work is done by extending the Keener’s approach from partial differential equations to partial integro-differential equations. Unlike the exiting literature, the newly proposed correction amounts (regarding the boundary level) are different across different scenarios and related to both the diffusion and jump parts. Numerical results indicate that such scenario-dependent correction does improve the approximation performance especially when the monitoring frequency is low and the boundary is nearby. Similar conclusions are obtained to price a discrete barrier option, and to show how marketability affect security values.
This is a joint work with S. Kou, S. F. Luo and H. C. Wong