First Passage Time Over Two Boundaries For A Diffusion Process With Jumps

• Main Authors: Wu, Mengchen, 吳孟臻
• Other Authors: Pai, Huiming
• Format: Others
• Language: zh-TW
• Published: 2012
• Online Access: http://ndltd.ncl.edu.tw/handle/42746282197824726424

碩士 === 國立臺北大學 === 統計學系 === 100 === This paper studies the first passage time over two boundaries for a double exponental jump diffusion process, which consists of a continuous part driven by a Brownian motion and a jump part with jump sizes having a double exponential distribution. Explicit solutions of the Laplace transforms, of both the distribution of the first passage times and the joint distribution of the process and its running maxima, are obtained. Because the double exponential jump diffusion process can solve the overshoot and undershoot problems, we can get closed-form solutions of the distribution of the first passage times. Finally, we use their Laplace transforms associated with a Laplace inverse algorithm to apply to pricing one-touch knock-in call option.