Affine Modeling of Credit Risk, Pricing of Credit Events, and Contagion

We propose a discrete-time affine pricing model that simultaneously allows for (i) the presence of systemic entities by departing from the no-jump condition on the factors’ conditional distribution, (ii) contagion effects, and (iii) the pricing of credit events. Our affine framework delivers explicit pricing formulas for default-sensitive securities such as bonds and credit default swaps (CDSs). We estimate a euro-area multicountry version of the model and address economic questions related to the pricing of sovereign credit risk. We find that both frailty (common factors) and contagion phenomena are important to account for the joint dynamics of credit spreads. Our results also provide evidence of credit-event pricing, which is at the source of substantial credit risk premiums, even for short maturities. Finally, we extract measures of depreciation-at-default from CDSs denominated in different currencies. This paper was accepted by Kay Giesecke, finance.

Introducing Fuzziness in CDS Pricing under a Structural Model

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.