Study Of The Credit Risk Pricing Problems With Transaction Costs

With the development of financial market, modern finance theory become more and moremature and perfect. In order to preventing, controlling and dissolving financial risks everywherewhich include market risk, operation risk and credit risk, all kinds of financial derivatives ap-pear unceasingly. So we must solve the problem of derivatives pricing and optimal investments.Although the classical Black-Scholes model has provided a pricing formula that is applicable toderivatives such as stocks, and calculates easily, however, its deduction and application are re-strained by some ideal hypothesis. So this paper try to extend the ideal market to more generalmarket. Based on the hypothesis in models such as paying transaction costs, existing interestrisks, credit risks and arising discontinuous jump about underlying assets'pricing process, webuild the model of several new type derivatives, and by using the method of PDE, the closed formsolution of the models is obtained.Options are the core tool of risk management. As a valid instrument that avoids risk andspeculative means, options are welcome to market practitioner and speculator. Early in 1973,Fischer Black and Myron Scholes proposed a famous option model–Black-Scholes model. After-wards , option pricing theory has developed quickly. and they become the significant componentof modern finance theory. This paper first introduced the emergence,development and actuality ofoptions pricing theory and the main contents.An application of the method to pricing option is designing and pricing the fund withpromised lowest return. As a new type financial derivative that is issued by some financial in-stitutions recently, it is designed for the investors who want to get relatively high return by takingsome market risk. The management company of the fund promise to provide the investors withprescribed lowest return and fixed portion of extra invest return. The investors need not to take thepossible invest loss of the company. In chapter 2, supposing that the market interest rate obeysthe general Hull-White Model we separately build the continuous-diffusion and jump-diffusionpricing model of a fund about promised lowest return with transaction costs. By transformingthe pricing units,the 2-D problem can be transferred to a 1-D PDE problem, and the closed formpricing formula can be thus obtained.In chapter 3, the problem comes from the pricing of the convertible bonds. As a mixturecontingence between bond and stock, it's very important for investors and issuers. Accuracypricing not only makes issuers to determine a fair price,but also protects the profits of investors.In the framework of Merton,this paper supposes that the market interest rate obeys the generalHull-White Model and pays off transaction costs, and we build the pricing model of convertible bond and the closed form solution is given by PDE method.Reset option is one of new type options. They have more chance of gains than other standardEuropean options. So they are welcome to market practitioner. Under this circumstance, wediscuss the option pricing model and pricing formula for two reset options that are reset optionswith predetermined dates and reset options with predetermined levels under stochastic interest ratein chapter 4.Lastly, a summary of this paper is made and further research directions are put forward.