The Pricing Of Catastrophe Bonds Based On The Fractional Brownian Motion And Poisson Process

The latest decades have witnessed catastrophes in almost every year, and the huge increasing frequency and intensity. In face of the increasing loss, due to the limitation of insurance companies and governmental relief, we have to figure out other methods to transfer catastrophe risks, therefore, capital market has attracted world's attention. Insurance securitization becomes a hot issue.In China, natural disasters are various and frequent with huge loss. From the worst flooding along Yangzi River in 1998 in a century, to the snow disaster in the south of China in the beginning of 2008, to 5.12 Wenchuan earthquake in the same year, to the recent months'especially big drought in the south west of China and to the 4.14 Yushu earthquake days ago, these raged natural disasters have brought huge economic loss as well as mental injury to Chinese people. However, because of weak risk management system, people are always ready to receive governmental aid or charity donation for free without purchasing insurance against natural disasters after disasters.In this paper, we mainly discuss the designing and pricing of catastrophe bond. The article is organized as follows. The section of"Introduction"focuses on literature review. We briefly introduce the status quo of some other countries'catastrophe risks as well as China, and the research situation about the pricing of catastrophe bond at home and abroad. The section"Fundamental Knowledge"introduces some basic knowledge about stochastic process and financial engineering such as frequently-used interest rate model. The section"The operating mechanism and classical pricing theory of Catastrophe Bond"simply introduces the operating mechanism and some classical pricing models of Catastrophe derivatives. The last section"the designing and pricing of Catastrophe Bond"is the core and innovation. Based on previous research, we suppose that the value of the loss index on catastrophe risk is driven by a fractional Brownian motion with Poisson jumps, and we introduce the stochastic rate model. We design two kinds of catastrophe bonds and price these bonds based on our assumptions.