Research On The Application Of Extended B-S Pricing Model In Catastrophe Risk Management

As a major agricultural country with a high incidence of natural disasters,China is facing severe forms of natural disasters and frequent occurrence of extreme weather and climate events.It is imperative to establish a multi-level market for disaster risk management.The current international operation of catastrophe options is not optimistic,and research on catastrophe options in China is only limited to the relevant theories of option design.Considering the slow development of the current Chinese catastrophe market and the long way to go in promoting the securitization of catastrophe risks,issuing financial instruments such as catastrophe options can effectively alleviate the pressure on traditional insurance and reinsurance markets,share catastrophe risks,and reflect the basic attributes of insurance loss compensation.It can also provide investors with a new way to allocate funds.Although the catastrophe option market in China has not been fully developed and the issuance of catastrophe options has a long way to go,studying the pricing of catastrophe options not only reflects the characteristics of a forward-looking new era,but also provides a theoretical basis for truly issuing catastrophe options and improving the catastrophe risk management system in the future.The main research work of this article is as follows:Firstly,we believe that the risk-free interest rate in the market is constant,assuming that the stock price process follows the Black Scholes model.There are two jump items in the process of setting the stock price.These two jump terms describe the impact of insurance claims and financial risks on option prices,respectively.The pricing formula for catastrophe options with jump diffusion processes is obtained through the martingale method of measure transformation.The relationship among time,stock strike price and catastrophe put option selling price is obtained through numerical simulation.We also analyzed the Greek alphabet value of catastrophe put option,in order to further understand the characteristics of catastrophe put option.secondly.Based on the constant interest rate scenario,we take into account the impact of interest rate fluctuations on stock prices.We extend the pricing formula for catastrophe options from the constant interest rate scenario to the random interest rate scenario.By introducing the Vasicek interest rate model with the advantage of mean reversion,we obtain the catastrophe option pricing formula with jump diffusion process when the interest rate is a stochastic process.Monte Carlo simulation and sensitivity analysis are made on the obtained catastrophic put option,and the basic attributes of catastrophic put option are also studied.Finally,based on the random interest rates mentioned earlier,interest rate volatility was further incorporated into the model setting.We assume that the interest rate follows the Hull White model,study the pricing formula of catastrophe put option when the interest rate and volatility are time dependent stochastic process,conduct numerical simulation and correlation coefficient sensitivity analysis on it,and obtain the trend of price change of catastrophe put option under different parameter values.Through the above work,this paper obtains the explicit solution formula of catastrophe put option with double jump term under the constant interest rate scenario and the stochastic interest rate scenario.In the constant interest rate scenario,we studied the correlation between exercise time,underlying stock price,and option price.Especially when the exercise time is determined,the stock price is inversely proportional to the option price.In order to further study the risk nature and trading strategy of catastrophe put option,the Greek alphabet value of catastrophe option is simulated and explained.Under the stochastic interest rate scenario,we study the pricing formula of catastrophe put option under the Vasicek model and Hull White model,respectively,and conduct numerical simulation on the correlation coefficient to analyze the relationship between the price of catastrophe put option and the related variables.