Attenuated Model of Pricing Credit Default Swap under the Fractional Brownian Motion Environment

Gu, Wenjing; Liu, Yinglin; Hao, Ruili

doi:10.4236/jmf.2016.62021

Cited by 4 publications

(4 citation statements)

References 15 publications

(19 reference statements)

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“…Compared to [7,15,16], the model in this paper can solve some inherent problems such as the asymmetry of market information flows and the low evaluations caused by inadequate disclosure of information. Of course, we are not able to examine the model in the real market as we are unable to get either the necessary market data or stability control in the form of interval numbers.…”

Section: Resultsmentioning

confidence: 99%

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Introducing Fuzziness in CDS Pricing under a Structural Model

Mei

2018

Mathematical Problems in Engineering

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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.

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Section: Resultsmentioning

confidence: 99%

“…In a fuzzy random environment, according to formulas (5), (15), and (18) and the nature of expectations, the following can be gotten:…”

Section: Theorem 6 the Right Point Of Level Set − Of The Fair Premiumentioning

confidence: 99%

Introducing Fuzziness in CDS Pricing under a Structural Model

Mei

2018

Mathematical Problems in Engineering

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“…Dong and Wang [21] assumed the intensities of the default times were driven by macro-economy described by a Markov regimeswitching model. Gu and Liu [22] established the attenuation model for the contagious risk and derived the pricing formula of CDS in the fractional dimension environment. Huang and Song [23] priced the basket CDS with counterparty risk under a multi-name contagion model.…”

Section: Introductionmentioning

confidence: 99%

Basket Credit Default Swap Pricing with Two Defaultable Counterparties

Chen

Xing

2022

Discrete Dynamics in Nature and Society

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In this paper, we study the basket CDS pricing with two defaultable counterparties based on the reduced-form model. The default jump intensities of the reference firms and counterparties are all assumed to follow the mean-reverting constant elasticity of variance (CEV) processes. Taking the Vasicek process which is a special case of CEV process as an example, the approximate analytic solutions of the joint survival probability density, the probability densities of the first default and the first two defaults can be solved by using PDE method. In addition, we also extend the Vasciek process to the Vasciek process with cojumps and obtain the approximate closed-form solutions of the relevant default probability densities. Then with the expressions of the probability densities, we can get the formula of the basket CDS price with two defaultable counterparties. In the numerical analysis, we do sensitivity analysis and compare the basket CDS prices under our model with that with only one defaultable counterparty. The numerical results show that our model can be applied into practice.

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“…Because it is impossible to assume that the impact of one firm's default to another firm's default keeps constant all the time, some authors introduced a hyperbolic function to reflect the attenuation effect in [8]. Recently, the cases that the interest rate satisfied the jump-diffusion process and the fractional Brownian motion were also discussed in [9]- [11]. The above conclusions on CDS were mostly obtained when the reference assets were the bonds.…”

Section: Introductionmentioning

confidence: 99%

Pricing Loan CDS with Vasicek Interest Rate under the Contagious Model

Liu¹,

Hao²,

Wang³

2016

JMF

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This paper mainly studies the pricing of credit default swap with the loan as the reference asset under the primary-secondary model. In the contract of credit default swap (CDS), we consider that the defaults of the counterparties are correlated with the stochastic interest rate following Vasicek model or the default state of the reference firm. We assume that the company's default is independent with the company's prepayment and obtain the pricing formulas of the loan and loan CDS.

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Attenuated Model of Pricing Credit Default Swap under the Fractional Brownian Motion Environment

Cited by 4 publications

References 15 publications

Introducing Fuzziness in CDS Pricing under a Structural Model

Introducing Fuzziness in CDS Pricing under a Structural Model

Basket Credit Default Swap Pricing with Two Defaultable Counterparties

Pricing Loan CDS with Vasicek Interest Rate under the Contagious Model

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