The Pricing Of Catastrophe Put Option With Stochastic Interest Rate

In recent years,the losses caused by catastrophes have increased dramatically all over the world.According to a report by Munich Reinsurance,the losses caused by natural disasters around the world will reach $210 billion in 2020,compared with $166 billion in 2019.The increase of catastrophe losses forces insurance companies to find ways to hedge catastrophe related risks.As a product of the integration of insurance market and financial capital market,catastrophe option has the advantages of low transaction cost,low moral hazard,high liquidity,open information and low default risk.Therefore,the pricing of catastrophe option has attracted an increasing number of attention in recent years.This paper studies the pricing of catastrophe put option with two kinds of stochastic interest rates.The first model considers the CIR Interest Rate without default risk,and the second model considers the Vasicek Interest Rate with default risk.We give the analytical expressions of two options prices and make numerical analysis.This paper is divided into three chapters:The first chapter is the introduction.Firstly,it introduces the research background of this paper.Secondly,it describes the research status of catastrophe option pricing model with and without default risk at home and abroad.Finally,the main models and results of this paper are summarized.In the second chapter,we study the pricing of catastrophe put option without default risk with CIR Interest Rate.In the first section,we give the general assumptions of the model,including the dynamic process of loss,interest rate and stock price.In the second section,we construct an equivalent martingale measure through measure transformation.In the third section,we obtain the analytic pricing formula of option under forward neutral measure.The fourth section is numerical analysis to study the changing trend of catastrophe put option price with different parameter values.In the third chapter,we study the pricing of catastrophe put option with default risk with Vasicek Interest Rate.In the first section,we give the model's structure and assumptions.In the second section,we decompose the option price by structural method,and transform the market measurement.In the third section,we give the analytical expression and specific proof process of the option price.The fourth section is numerical analysis,which discusses the change trend of catastrophe put option price with different parameter values.