Pricing European Vulneralbe Options Under Ambiguity Framerwork

Economic globalization has not only gradually made the financial markets of each country into a closely related economic community,but also greatly promoted the economic development of each country.Behind the prosperity,global financial markets are also facing challenges from unknown events.Once a serious social event occurs,it will have a serious impact on the global financial market.For example,in early 2020,the crude oil price war between Saudi Arabia and Russia caused the stock indexes of many countries in the world to plummet.Coupled with the impact of the Novel coronavirus pneumonia epidemic,the stock markets of several European countries have melted down one after another,and the US stock market has melted down twice in a week.It cannot help recalling the situation in 2007 when the subprime debt crisis finally broke into a global financial tsunami.When market participants are facing serious social events,their investment attitudes will be seriously ambiguous.Ambiguity is the subjective attitude of market participants in the face of unknown information.Subjective ambiguous attitudes of market participants will affect the valuation of financial products and financial derivatives.The initial research on the pricing of options was based on the assumptions that the risk-neutral environment or the complete market.In these assumptions,ambiguity is considered purely as risk,but in fact,ambiguity goes beyond the scope of risk.Besides these assumptions also ignores the impact of crisis events on pricing models.There have been many studies on ambiguity which is also called Knight uncertainty and many scientists have introduced ambiguity to the pricing of financial products such as European call options and convertible bonds.In this paper,we research on a special kind of options," vulnerable options",which are exposed to counterparty credit risk,and explore the European vulnerable options pricing model under ambiguity.The research in this paper mainly includes two complete and independent models,which respectively use different methods to take the ambiguity into European vulnerable options pricing model,and finally they both obtain a closed form integral formula for European vulnerable option pricing under the ambiguity framework.The first model is European vulnerable options pricing model based on Choquet ambiguity,and the other model is European vulnerable options pricing model with ambiguity about Heston’s stochastic volatility,corresponding to Chapters 2 and Chapters 3 in this paper,respectively.