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

Abstract

In the real world, corporate defaults will be affected by both external market shocks and counterparty risks. With this in mind, we propose a new default intensity model with counterparty risks based on both external shocks and the internal contagion effect. The effects of the external shocks and internal contagion on a company cannot, however, be observed, as uncertainty in the real world contains both randomness and fuzziness. This prevents us from determining the size of the shocks accurately. In this study, fuzzy set theory is utilized to study a looping default credit default swap (CDS) pricing model under uncertain environments. Following this, we develop 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, and that the credit spreads, relative to the degree of external shock fuzziness, are much more sensitive. Nevertheless, for a certain degree of fuzziness in the market, credit spreads, relative to changes in counterparty risk, are much more sensitive. Using random analysis and fuzzy numbers, one can think of even more uncertain sources at play than the processes of looping default and investor subjective judgment on the financial markets, and this broadens the scope of possible credit spreads. Compared to the existing related literature, our new fuzzy form CDS pricing model with counterparty risk can consider more factors that influence default and is closer to the reality of the complexity of the dynamics of default. It can also employ the membership function to describe the fuzzy phenomenon, enable the fuzzy phenomenon to be estimated in two kinds of state, and can simultaneously reflect both the fuzziness and randomness in financial markets.

Fuzzy Random Option Pricing in Continuous Time: A Systematic Review and an Extension of Vasicek’s Equilibrium Model of the Term Structure

“…However, there are several nuances to consider in this regard. For example, [68,69] extend FROPCT to currency options using the analytical framework provided by Garman and Kolhagen [99], and [73] extends the Asian option valuation formula of Kemma and Vorst [100]. Additionally, within the framework of geometric Brownian, there are 6 works that assume that various parameters of the Margabre exchange valuation model [101] and Geske's compound option model pricing formula [101] are given by fuzzy numbers.…”

“…In some cases, especially in articles that are based on the standard BSM model, issues associated with fuzzy analysis are refined. These issues may embed, such as defuzzification [33,36,56,57,68,71] or the construction of membership functions for the inputs of the pricing formula or the final price of the asset [25,31,32,36,40,[50][51][52].…”

“…We have not retrieved any fuzzy-random approach to equilibrium models of yield rates and to the option pricing formulas that can be derived from these models. We can only outline [68], which assumes a crisp modelling of the term structure with the model by Cox-Ingersoll and Ross [15] to free the risk interest rate in the evaluation of credit default swaps, but the observed short rate is a fuzzy number. This fact motivates the extension developed in this section for the one-factor model for the yield curve model by Vasicek [12] to the presence of fuzziness in the parameters.…”

The study on risk avoidance of transaction default based on the herding effect

“…Therefore, Jarrow and Yu (2001) further proposed the intensity-based model of circular default, assuming that there is a close economic relationship between company A and B, when one company defaults, another company will be affected, there will be a big jump in the intensity of its default. The literature on circular default can also be found in Wu et al (2016Wu et al ( , 2018, Liang et al (2014), Zhang et al (2018) and so on.…”

Non-Homogeneous Semi-Markov and Markov Renewal Processes and Change of Measure in Credit Risk

“…The above publications of non-homogeneous semi-Markov and Markov renewal processes for credit risk was followed by quite a lot of literature by the same and other authors in credit risk and related subjects. For example, from recent years, see Huang [13], D' Amico et al [14,15], D' Amico [16], Magni et al [17], Wu et al [18,19], Puneet et al [20], De Blasis [21]. In D' Amico et al [22], bivariate semi-Markov processes are introduced for the pricing of Credit Default Swaps (CDS).…”