Catastrophe Option Pricing And Catastrophe Risk Management Under Jump Diffusion Model

In recent years,the frequent occurrence of natural disasters in China has seriously affected the development of China's economy and caused huge losses to people's lives.In order to reduce the losses caused by catastrophe,the risk capacity of catastrophe risk management is being strengthened.People use mathematics,finance and other knowledge to actively develop catastrophe insurance derivatives market,and strive to learn from the experience of catastrophic risk management in developed countries,and on this basis,extract the essence of the catastrophe derivatives pricing method suitable for China's financial market.With the rapid development of China's economy and the deepening of opening up,the investment and operation of the insurance industry are more closely linked with the capital market.Mutual support and influence will be more significant in the future.In some developed countries and regions,catastrophe risk has been transferred to the capital market through the transaction channel of derivatives of catastrophe insurance.The key is how to reasonably determine the price of derivatives of catastrophe insurance.This paper analyzes the catastrophe risk at home and abroad,designs catastrophe option model,and price it.The first task of catastrophe option pricing is how to establish catastrophe option model.The study of catastrophe option is beneficial to catastrophe risk management,and can be used to price catastrophe option.Firstly,this paper introduces the background,significance and related theoretical knowledge of catastrophe derivatives Secondly,based on Poisson process,the catastrophe option model under jump diffusion is constructed.By using independence lemma and transfer probability,it is proved that the model has Markov property of linear jump diffusion process,and catastrophe option is regarded as Asian option.PDE method is used to change pricing unit,and the pricing result of semi explicit solution of arithmetic average Asian option pricing formula under jump diffusion model is given Finally,the application of catastrophe option pricing in risk management under jump diffusion model is studied.