A Model for Counterparty Risk with Geometric Attenuation Effect and the Valuation of CDS
Yunfen Bai (1, 2), Xinhua Hu (1), Zhongxing Ye (1) ((1)Department, of Mathematics, Shanghai Jiaotong University; (2)Department of Mathematics,, Shijiazhuang College)
TL;DR
This paper introduces a geometric attenuation model for counterparty risk, capturing how default impacts diminish over time, and applies it to valuing CDS premiums with derived default distributions.
Contribution
It proposes a novel geometric attenuation function to model default impact decay and derives default time distributions for CDS valuation.
Findings
Derived joint and marginal default time distributions
Provided a method for fair CDS premium valuation
Captured dynamic default impact attenuation
Abstract
In this paper, a geometric function is introduced to reflect the attenuation speed of impact of one firm's default to its partner. If two firms are competitions (copartners), the default intensity of one firm will decrease (increase) abruptly when the other firm defaults. As time goes on, the impact will decrease gradually until extinct. In this model, the joint distribution and marginal distributions of default times are derived by employing the change of measure, so can we value the fair swap premium of a CDS.
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Taxonomy
TopicsCredit Risk and Financial Regulations · Stochastic processes and financial applications · Banking stability, regulation, efficiency