Pricing Vulnerable Options When Corporate Liabilities Are Random

Credit default risk has always been a hot topic in finance.Credit default events emerge in an endless stream,especially in the outbreak of the subprime mortgage crisis in 2007,then subsequent spread to the global financial crisis.Financial derivative default plays an important role in the Credit default events.Vulnerable option is a kind of financial derivative product.Because it has the characteristics of credit risk,it can also be called an option with credit risk.Its importance has attracted the research interest of many scholars.The initial research on option pricing was mostly carried out under the assumption that asset prices based on the general geometric Brownian motion of asset prices.However,the real financial market is complex and constantly changing.The price of vulnerable options is not only affected by the price of the underlying asset,but also by the price of the counterparty assets.Therefore,a large number of scholars have studied the pricing of vulnerable options under different models,including the jump-diffusion model and the stochastic volatility model under the assumption that the company's liabilities are constant.However,it is well known that the company's liabilities are constantly changing.So we study the vulnerable option pricing under the jump-diffusion model and the stochastic volatility model when the company's liabilities are stochastic.The remainder of this paper is organized as follows.In chapter 2,we discuss the pricing of vulnerable options with correlated credit risk under jump-diffusion processes when corporate liabilities are random.In chapter 3,we discuss the pricing of vulnerable options with stochastic volatility when corporate liabilities are random.The two parts all include the background of the model establishment,some assumptions,the established model and so on.