Introducing Fuzziness in CDS Pricing under a Structural Model

Abstract

OTC credit derivatives are nonstandardized financial derivatives which have the following characteristics. (1) Information on trades is not public. (2) There is no performance guarantee from the stock exchange. (3) The bigger the risk in performance, the bigger the price floating. These result in an asymmetry of market information flow and this asymmetry acts as a decisive factor in the credit risk pricing of financial instruments. The asymmetry of market information flows will lead to obvious fuzziness in how counterparty risks are characterized, as in the process of valuing assets when discontinuous jumping takes place. Accurately measuring the amplitude and frequency of asset values when influenced by information asymmetry cannot be arrived at just by analyzing the random values of historical data. With this in mind, this paper hypothesizes both asset value jump amplitude and frequency of random parameters as a triangular fuzzy interval, i.e., a new double exponential jump diffusion model with fuzzy analysis. It then gives a credit default swap pricing formula in the form of fuzziness. Through the introduction of fuzzy information, this model has the advantage of being able to arrive at results in the form of triangular fuzziness and, consequently, being able to solve some inherent problems in a world characterized by asymmetry in the flow of market information and, to a certain extent, the inadequate disclosure of information.

Pricing of Basket CDS with Bilateral Default Risk under Vasicek Model with Circular Contagion

“…Kijima and Muromachi [6] considered the pricing of the k-to-default basket CDS, but they did not give a clear solution. Wu et al [7] proposed a new model for evaluating the value of credit default swap contracts subject to multiple credit risks. Tey showed that default dependence has a signifcant impact on CDS pricing.…”

Basket Credit Default Swap Pricing with Two Defaultable Counterparties

“…Chen and He [6] proposed the multi-scale stochastic volatility (SV) model to price a CDS. Based on the structural model and introducing the concept of fuzziness, Wu et al [7] proposed a new double exponential jump diffusion model with fuzziness for CDS pricing.…”

“…Kijima and Muromachi [17] considered k th -to-default basket CDS pricing, but they did not give the explicit solution. White [7] presented a new model for valuing a CDS contract which was affected by multiple credit risks. ey showed that the default dependency had a significant impact on CDS pricing.…”

Credit default swap pricing with counterparty risk in a reduced form model with a common jump process

“…Chen and He [3] proposed the multiscale stochastic volatility (SV) model to price the CDS premium. Under the framework of structural model, Wu et al [26] proposed a new double exponential jump-diffusion model with fuzziness for CDS pricing. He and Lin [11] derived an analytical approximation for the price of a CDS contract price by assuming that the reference asset followed a regime switching Black–Scholes model.…”