Research On Credit Derivatives Pricing And Optimal Investment Based On The Option Pricing Theory

Credit risk, also called default risk, is the distribution of financial losses due to the changes in the credit quality of a counterparty in a financial contract. Its range includes failure to service and liquidation, agency down grades and so on. Along with the global relaxation of financial restriction and the rapid progress of corporate bond market, the damage caused by credit risk is an issue of great concern in finance. In 2008, the credit default problem attracted global attention again due to the worldwide financial crisis. At the same time, although the corporate bond market of China grows rapidly, it's also lagging if comparing with the developed countries. Thus the research about credit derivatives pricing and optimal investment has important theoretical and Practical meaning to improve the competition of our country's finance institute. The major achievements are summarized as follows:Chapter 1 is the introduction part. The author exposits the significance of the current topic, literature review, and the framework of the whole paper.Chapter 2 presents a trinomial tree model for pricing forward credit default swaps (CDSs), and CDS options of American and Bermudan styles subject to equity and market risk. Interest rates are assumed to follow a mean-reverting square root process. The reduced-form approach is generalized to include a constant elasticity of variance (CEV) process for equity prices prior to default, which is capable of reproducing the volatility smile observed in the empirical data. Based on the empirical results in Duffie et al (2007) (J. Fin. Econ. 83 (3): 635-665, 2007), the default intensity is specified as a function of time, stock prices, and interest rates. The call and put features embedded in CDSs as well as the correlation between interest rates and equity prices are also considered. Illustrative examples show the use of the model and numerical results explain the impact of different parameters on the prices of forward CDSs and CDS options.In Chapter 3 we propose a lattice framework for valuing convertible bonds (CBs) and asset swaps on CBs with market risk and counterparty risk, where interest rates are assumed to follow a mean-reverting square root process. The CB considered here has call feature that allows the issuer to buy it back for a predetermined price. The reduced-form approach is similar to Chapter 2. Similar to Carayannopoulos et al (2003), we also strip the value of the CB into a straight bond part and a call option part. When valuing the CBAS, we take the counterparty risk embedded in the interest rate swap into consideration. Our approach is entirely based on observables such as equity prices and interest rates, and can be easily implemented when pricing CBs and other related instruments. From the results of the numerical experiment, we find that the correlation between interest rates and equity prices has a slight impact on the values of CB and its bond component, and that the leverage effect and counterparty risk play important roles in determining the values of asset swaps.Chapter 4 studies debt holders' belief updating, valuation of corporate debt, and equity owners' financing decisions during financial distress under asymmetric information. This is done within a continuous-time framework, where the relevant state variable is assumed to follow an Arithmetic Brownian motion (ABM). ABM can take negative values and has very realistic feature compared with Geometric Brownian motion (GBM). Using Chapter 11 of U.S. Bankruptcy Code as a costly screening device, we can characterize which firm will choose private workouts (in the form of strategic debt service) and which will choose to file for the Chapter 11 Bankruptcy procedure (in the form of debt-equity swap) when the firm is in financial distress. Using arguments similar to equilibrium refinements, we give a clear picture of how debt holders' beliefs about the firm's types are updated according to the state variable and the firm's default behavior, and describe optimal strategies of both parties under those beliefs. We also provide an approximate solution to the debt pricing problem under asymmetric information.Chapter 5 examines the impact of asymmetric information on firms' investment and financing decisions when firms issue equity or debt to cover the capital outlay. We assume that firm insiders exactly know the firms' growth prospects, but outside investors do not know. Our analysis shows that, under equity or debt financing, there exists a costly sig- naling equilibrium, in which firm insiders can communicate their private information to outside investors and avoid selling underpriced equity or debt by changing the timing of investment. It is demonstrated that informational asymmetry significantly erodes the option value of waiting to invest and leads firms with good growth prospects to speed up investment. Comparative static analysis shows that the model is consistent with the available empirical evidence.In Chapter 6 we conclude the paper and provide the framework of the future research.