Credit Spread Option Pricing Under The Jump Diffusion Model

Option is a financial derivatives which are produced on the basis of futures. This kind of financial Derivative instrument’s greatest charm that can make the options buyer will risk locking in a certain range. It has been widely used in hedging, risk management. The banking sector in China has developed rapidly in recent years. With credit riksk have also begun gradually. Most of investors have all been faced the unprecedented challenge by credit risk. Credit risk is a serious threat to the stable development of the financial and economy. Credit derivative products resolve partially this intractable problem. Credit spread option is one of the representative of the credit derivatives, Which is the most sensitive one to the change of interest rate among credit derivatives.Credit spread is used to compensate for investor on the basis of underlying asset’s default risk which is the interest margin higher than the risk-free interest rate. The so-called is defined as yields on loans or securities with the corresponding difference between the risk-free rate of return. It can be a good measure of credit risk. As an important means of risk control credit spread option’s pricing is also the focus of attention problems. And also has a strong demand for market. which gradually becomes a main topic in the field of option pricing. But in recent years, A number of large financial emergencies occured. These unusual events lead to asset volatility, Resulting in jumping phenomenon. Classic Black-Scholes model is already unable to cope with the current economic situation. It must be used to a jump-diffusion model. Such model is better to adapt to changes in present market.This paper is established on the condition that risk-free interest rate and credit spread model all accord with Vasicek model which proposed by Longstaff and Schwartz in 1995. Then extend this model to a jump-diffusion model to solve the problem of credit risk. Main work of the thesis are as follows:Chapter 1 firstly provides an introduction to the necessity of the research on the credit spread options. Furthermore, We introduce the credit spread option pricing research at home and abroad. Chapter 2 discuss the pricing of European standard credit spread option and American standard credit spread option under the interest rate and spread all with jump respectively. In this chapter, By applying Fourier inversion transform, Feynman-Kac theorem and practical differential equation. We get the closed form about the European credit spread put option prices. For Amer-ican standard credit spread put option prices. And take measures to solve the problem include the compound option approach which proposed by Geske and Johnson.Using 2 point G-J law to discretization. Finally some numerical examples are provided by parameters on the effect of Eu-ropean credit spread call option prices and get some conclusions. Chapter 3 we discuss mainly the pricing of an Asian-style credit spread option under the model with jump on the Chapter 2. The pricing of fixed Eurpean-style geometric-average Asian credit spread option, The same to the Chapter 2.We derive firstly the closed-form solution of the price for the geometric-average option which is used as a control variable to simulate the approximation of the arithmetic-average op-tion.Then we apply the reduced variance technique to simulate the price of the arithmetic-average Asian credit spread option. Finally, Sensitivity analysis is conducted through numerical examples. In Chapter 4 we sum our main conclusions and suggestions for further research.In the end, It is worth noting that study on pricing of credit spread option based on jump diffusion model. Not only avoid the risk of capital operation effectively and attract investors. But also promote the prosperity of the financial markets. and improve management decision-making capacity.