A New Default Intensity Model with Fuzziness and Hesitation

Abstract

With the increased financial market volatility, corporate defaults will suffer from the double impact of the external shocks and internal contagion effects. In the existing stochastic default intensity models, the valuation of sensitivity parameters requires a lot of historical data, however, the limited market data does not guarantee the accuracy of parameter estimation, meanwhile, due to the people have a lot of fuzziness and hesitation judgements on the default process, it is necessary for us to let the corresponding random parameter of the default intensity to be a triangular intuitionistic fuzzy interval value. In this paper, we propose a new default intensity model based on the external shocks and internal contagion effects, and introduce the triangular intuitionistic fuzzy numbers into the credit default swaps (CDS) pricing modeling to describe the fuzziness and hesitation of the default process. In the end, we get a new fuzzy form pricing formula for CDS, and by the simulation analysis, we obtain that, all kinds of fuzziness and hesitation of the market have significant impact on credit spreads, and a model result with a consideration of the fair price of CDS in a fuzzy random environment including a pure random environment result. Compared with the existing stochastic model, these proper interval results can offer the investors more flexible options and can more reflect the impact of market environment on credit spreads.

A reduced-form intensity model containing noise interference

“…Wu (2015) discussed the problem of credit risk measurement under asymmetric information. With the deepening of research, scholars pay more and more attention to the important role of asymmetric information in the study of economic and financial problems, studies such as Wu and Zhuang (2015), Wu, Liu, Wang, and Zhuang (2016a), Wu, Zhuang, and Li (2016b), Wu, Wang, Liu, and Zhuang (2017), Wu and Zhuang (2018).…”

The Total Return Swap Pricing Model under Fuzzy Random Environments

“…He described the evolution of credit migration of a defaultable bond as an inhomogeneous semi-Markov process with fuzzy states, and investigated the asymptotic behavior of the survival probability in each fuzzy state given in the absence of default. Wu et al [27][28][29] proposed a reducedform intensity-based model under fuzzy environments and presented some applications of this methodology for pricing defaultable bonds and credit default swap (CDS). However, no scholars have considered the total return swap pricing model in a fuzzy random environment, even though this has become a significant problem to be studied.…”

Pricing for a basket of LCDS under fuzzy environments

“…There is some literature concerning option pricing in a fuzzy random environment (Ma et al 2012 ; Simonelli 2001 ; Yoshida 2003 ; Wu 2004 ; Xu et al 2009 ; Zhang et al 2010 , 2013 ) and the application of uncertain information in other fields (Jiang et al 2016a , b ; Deng 2015 , 2017 ; Ning et al 2016 ; Akyar 2016 ; Wang et al 2014 ). There is, however, little research into the pricing of credit derivatives when a fuzzy environment is introduced (Agliardi and Agliardi 2009 ; Wu and Zhuang 2015 ; Wu et al 2016 ).…”