Fuzzy defaultable bonds

A New Default Intensity Model with Fuzziness and Hesitation

“…However, as far as we know, there are few about credit risk analysis and derivatives pricing model under fuzzy environments. E.Agliardi and R.Agliardi [19][20] first proposed a structural model for defaultable bonds in a fuzzy environment, they assumed the assets value is a fuzzy stochastic process, the assumption is related to the investors' subjective belief about the reliability of the accounting data of the firm, and the duration analysis show that the fuzziness of the stochastic underlying assets have material impact on the term structure of credit spreads. Vassiliou 21 proved that a fuzzy market is viable if and only if an equivalent martingale measure exists, and constructed the forward probability measure, described the evolution of credit migration of a defaultable bond as an inhomogeneous semi-Markov process with fuzzy states, and investigated the asymptotic behaviour of the survival probability in each fuzzy state given in the absence of default.…”

“…As pointed out in the above section, the company's default will be subjected to the external shocks and counterparty risk, therefore, inspired by Bai 23 and Leung and Kwork 24 , we will propose a new looping default intensity model with attenuation effects based on the external shocks and contagion effects. Meanwhile, inspired by E.Agliardi, R.Agliardi 19 and Wu, Zhuang 22 , we will introduce the fuzzy analysis into the credit derivatives pricing process, nevertheless, the literatures 19,22 both employed the triangular fuzzy numbers to describe the fuzzy phenomenon, since there is only one membership function, result in the fuzzy phenomenon can only be estimated in two kinds of state: the possible degree and impossible degree, and can not reflect the degree of hesitation in the fuzzy phenomenon, but hesitation in the pricing process or in the market is objective existence, becomes an another important influence factor in the pricing process of the credit derivatives, such as the application of hesitation in product design can be found in Dou, Zong and Li 25 . However, for the triangular intuitionistic fuzzy numbers, there are membership function and non-membership function to simultaneously describe the fuzzy phenomenon, enable the fuzzy phenomenon can be estimated in three kinds of state: the possible degree, impossible degree and hesitation degree, this characterization method can reflect the degree of hesitation in the fuzzy phenomenon, that is, the triangular intuitionistic fuzzy numbers can be a good solution to the problem of hesitation characterization.…”

“…However, for the triangular intuitionistic fuzzy numbers, there are membership function and non-membership function to simultaneously describe the fuzzy phenomenon, enable the fuzzy phenomenon can be estimated in three kinds of state: the possible degree, impossible degree and hesitation degree, this characterization method can reflect the degree of hesitation in the fuzzy phenomenon, that is, the triangular intuitionistic fuzzy numbers can be a good solution to the problem of hesitation characterization. Therefore, in this paper, we will introduce the triangular intuitionistic fuzzy numbers to describe the fuzziness and hesitation of the default process, rather than the triangular fuzzy numbers method in E.Agliardi, R.Agliardi 19 and Wu, Zhuang 22 , and construct the pricing model for CDS. The main contributions of this paper can be summarized as: 1.Based on the external shocks and internal contagion effects, we propose a new default intensity model with attenuation effects, compared with the literature Bai 23 and Leung and Kwork 24 , our intensity model can consider more default influence factors, and more close to the reality of the complexity of the dynamic of default.…”

“…The main contributions of this paper can be summarized as: 1.Based on the external shocks and internal contagion effects, we propose a new default intensity model with attenuation effects, compared with the literature Bai 23 and Leung and Kwork 24 , our intensity model can consider more default influence factors, and more close to the reality of the complexity of the dynamic of default. 2.We introduce the triangular intuitionistic fuzzy numbers for the calculation of the default probability, compared with the literature E.Agliardi, R.Agliardi 19 and Wu, Zhuang 22 , we can employ the membership function and the non-membership function to simultaneously describe the fuzzy phenomenon, enable the fuzzy phenomenon can be estimated in three kinds of state: the possible degree, impossible degree and hesitation degree. 3.Compared with the existed models, we construct the pricing model for CDS under fuzzy environments for the first time, and get the credit spreads which can simultaneously reflect the fuzziness and the hesitation.…”

A New Default Probability Calculation Formula and Its Application under Uncertain Environments

“…This prevents us from determining the size of shocks accurately. Therefore, inspired by [14][15][16][17][18], fuzzy set theory is adopted to study a looping default credit default swap (CDS) pricing model under uncertain environments. Following this, we set up a new fuzzy form pricing formula for CDS, the simulation analysis of which shows that all kinds of fuzziness in the market have a significant impact on credit spreads.…”