Study The Pricing Model Of Unf- Unded Credit Derivatives Under Fuzzy Random Environments

Credit derivatives pricing is a mathematical modeling process from social reality, its existing and depending market environments have various random and fuzzy characteristics, and on the other hand, because human minds that describe and build pricing model are ambiguous, the thinking process of mathematical modeling has the features of randomness and fuzziness. When combining randomness and fuzziness, a new subject fuzzy random comes into being, the research of which provides a new theoretical basis for credit derivatives pricing theory, and is a useful and necessary supplement of the traditional theory of pure random credit derivatives pricing. This paper, based on fuzzy random theory, studies unfunded credit derivatives pricing model that can cash keep flow remain in the subprime crisis under fuzzy random environments.In this study, we construct and verify the pricing formula of unfunded credit derivatives based on the intensity-based model and structural model of credit risk analysis in the fuzzy random environments. After the US debt crisis, people generally questioned the company’s default information disclosure, and then the problem of fuzzy judgment has caused wide attention, therefore, this study starts with the assumption that the Cox process (which was proposed by Lando) is a fuzzy triangle number to the right, further more, according to the specific default factors to construct a new intensity model, that is, based on the external market impact and the internal contagion effect, we construct a new default intensity model with counterparty risk, and introduce the fuzzy analysis into the CDS pricing. However, intensity-based model deficiencies are lacking explanatory power to exogenous default mechanism and ask for more historical data, so we make TRS and the synthesis CDO pricing through the structure model and the fuzziness in the process of asset movements, meanwhile, a Fuzzy Copula function is constructed based on the fuzzy process theory, enable us to consider the effect of the environmental fuzzy on the credit spreads and avoid the result of the model becomes an interval. Then, we introduce the hesitation (the fuzzy phenomenon corresponding to the degree of hesitation) to the intensity-based model and structural model, and use the triangular intuitionistic fuzzy numbers to describe the corresponding hesitation in the process of credit derivatives pricing, and the fuzzy form pricing formulas of CDS and LCDS are constructed. Finally, we make a conclusion and point out the future research direction. In this study, on the basis of credit derivatives pricing modeling and fuzzy random theory, we do some research on unfunded credit derivatives pricing model. Its main conclusions are as follows:Because of the characteristics of OTC trading of credit derivatives, lead to a lack of transparency in transactions, and cause there is a vague uncertainty about the credit default intensity of the investors to the counterparty. Thus, we assume that the Cox process as a fuzzy stochastic process which is proposed by Lando. and the left divergence is less than the right, the assumption is related to the investors" subjective belief about the evolution of the state of financial environments over time:they tend to shift the firm’s default probability to the right, because the published financial situation of firm is more likely to be overstated than understated as misreporting or deceiving behavior is a possibility, especially in a financial crisis. Moreover, we adopt the fuzzy set theory to present a fuzzy default probability and default loss rate, and puts them into default debt and credit derivatives pricing. Setting the default intensity as a fuzzy form can make people’s subjective judgment on the market conditions combine with the credit spreads, and add the empirical value of the pricing to the model results.We build a new default intensity model including a counterparty risk on the basis of market external impacts and internal contagion effects, this is an improvement on Bai to consider only the risk of counterparty, and an improvement on Leung & Kwork to consider only the risk of external shocks. Then, we introduce the fuzzy analysis into the CDS pricing, that is, employ the triangular fuzzy numbers to study the CDS pricing problem under a fuzzy random environment. Further more, the attenuation effect is introduced into the intensity model, and taking into account the impact of the fuzziness and hesitation of the market environments on credit spreads, adopt the triangular intuitionistic fuzzy numbers to the CDS pricing, and derive a fuzzy form pricing formula of the CDS. Last, through the simulation analysis, we obtain that, all kinds of fuzziness of the market have significant impact on credit spreads, and the credit spreads relative to the fuzzy degree of external shocks are much more sensitive, however, in the condition of a certain degree of fuzziness in the market, the credit spreads relative to the change of counterparty risk are much more sensitive, meanwhile, we conduct the hesitation sensitivity analysis, the results show that with the increase of people’s hesitation, the fuzzy price range also gradually become bigger, it shows that people can improve the accuracy of credit spreads by reducing the degree of hesitation.As the financial markets are always in oscillation, the asset value may appear discontinuous jump process. But the magnitude and frequency of the value jump is not fixed, that is, people to the jump process of the assets has a certain fuzziness. Therefore, we build a new double exponential jump diffusion model with fuzzy information, and then the fuzzy pricing formula of TRS with fuzzy analysis is given. Through the simulation by R software, the results show that with the increase of market information fuzziness to investors, the fuzzy price range will gradually increase, and with the increase of the subjective judgment of investors, the price range will be gradually reduced. Compared with the existed models, using the fuzzy random theory to describe the movement of the assets can reduce the predictability of default in the structural model by imperfect information collection (i.e. fuzzy information).Because of the existence of the "correlation smile" in the CDO tranches, which the results are calculated by the One-factor Copula model, the correlation coefficient in the standard model is assumed to be a triangular fuzzy random variable, compared with the Schloegl L.’two states random coefficient model and the X.Burtschell’ three states random coefficient model, we set the correlation coefficient of Copula model is an interval value, this special assumption can consider the fuzziness in the process of estimation of the parameters. Moreover, we build a new One-factor Gaussian Copula model with fuzzy analysis, give the interval form joint default probability and default loss rate, and apply this model to synthetic CDO pricing. Finally, the simulation analysis of the cumulative loss distribution function with different reliability is given by using MATLAB simulation technology, and the rationality of the model is verified.Taking prepayment risk of reference entity of LCDS, as well as the fuzziness and hesitation of investors to the prepayment of borrowers, we discuss the first default pricing of a basket of LCDS in a fuzzy environment with stochastic analysis and triangle intuitionistic fuzzy set theory. Through the fuzzification of sensitivity coefficient in the prepayment intensity, and describes the dynamic features of mortgage housing value with One-factor Copula function, we put out a fuzzy pricing formula for the first default of a basket of LCDS. Using computer simulation, and conduct the hesitation sensitivity analysis, the results show that the model results of the pure random environments are included in the LCDS fair premium of the fuzzy random environments, and the investors can improve the prediction accuracy of the fuzzy price of LCDS in a fuzzy environment via decreasing the hesitation degree. Compared with the existing models, the proposed model can simultaneously consider the fuzziness and hesitation in the prepayment.