Spread Option Pricing Based On Counterparty Default Risk

Financial markets are changing with each passing day and financial elements are closely related.Spread option can connect a number of products.Besides,financial risk problems keep emerging.As an OTC option,spread option carries default risk,and its real return should be less than the theoretical return.Therefore,this thesis focuses on studying the pricing of spread option based on the counterparty default risk.The first chapter sorts out some documents on spread option pricing and counterparty default risk.In the model part,in order to reflect the description of default risk,this paper chooses to use a reduced model,and we use OU process to represent the risk.when setting the model,considering that the price process of many underlying assets may have a jumping process,the second chapter of this paper discussed the pricing problem of the spread option with counterparty default risk under BS model.The third chapter added a jumping process to the price process of the two underlying assets of the spread option based on the second chapter model.Since the spread option itself contains two basic assets,its payment function of ordinary option is more complex.However,when calculating the option pricing expressions under the two models,it can be found that if the strike price of the spread option is equal to 0,the model can be simplified and solved with the aid of measure transformation,properties of moment generating functions and other knowledge.However,when strike price of the spread option witch unequal to 0,the measure space that the strike price is equal to 0 is still used,but it needs to use the method of constructing multiple integrals,combined with the knowledge of characteristic function and complex function,etc.,to calculate the specific expression of option pricing on the spread of the default risk with the counterparty.When calculating the option pricing expressions under the two models,it can be found that if the strike price of the spread option is equal to 0,analytical solution can be solved through measure transformation,PDE and other knowledge.However,when strike price is a number which unequal to 0,the measure space that the strike price is equal to 0 is still used,and the knowledge of characteristic function and complex variable function is combined.In Chapter Four this paper conducts financial simulation on the four models in the second chapter and the third chapter.After that,we use correlation analysis so that we can study the influence of some important parameters on the pricing of the spread option based on the counterparty default risk,and the corresponding explanation of economic significance is given.At the same time,we also compare the difference of several models,studies whether the strike price is 0 and whether the jump process has an impact on the pricing of the spread option.We can get some specific expressions for pricing options.The last chapter reviews the main points of the thesis and gives the prospect of future research.