Modeling basket credit default swaps with default contagion

Abstract

The specification of a realistic dependence structure is key to the pricing of multi-name credit derivatives. We value small k th-to-default CDS baskets in the presence of asset correlation and default contagion. Using a first-passage framework, firm values are modeled as correlated geometric Brownian motions with exponential default thresholds. Idiosyncratic links between companies are incorporated through a contagion mechanism whereby a default event leads to jumps in volatility at related entities. Our framework allows for default causality and is extremely flexible, enabling us to evaluate the spread impact of firm value correlations and credit contagion for symmetric and asymmetric baskets.

Weak Convergence of Path-Dependent SDEs in Basket Credit Default Swap Pricing with Contagion Risk

“…Denote by N µ,h n := N µ (V h , nh). Using the Euler recursive formula (6) and Assumption 2, we have…”

“…Furthermore, we include contagion risk in the model, in which the default of a name in the reference portfolio causes a jump increase of volatility of the counterparty, which increases the default probability of the counterparty. The aforementioned model, for instance [6], incorporates both counterparty risk and contagion risk, whereby it can realistically explain the severe difficulties experienced by some seemingly defaultremote banks underwriting super senior tranche CDOs (collateralized debt obligations) during the financial crisis of 2007-08.…”

Stochastic Evolution Equations in Portfolio Credit Modelling

“…Other recent papers using a structural approach include [16], [17], [8] and [7]. We aim to develop a model which can allow pricing of exotic options on CDO tranches and note that there has been some discussion of such products in [22], [24].…”

An Entropy Model of Credit Risk Contagion in the CRT Market

“…A number of recent studies have considered the credit risk contagion of the CRT market. Haworth and Reisinger [11] proposed a numerical approach to modeling firm value dynamics and the default event, enabling the valuation of basket credit default swap spreads in a first passage framework with both asset correlation and default contagion. Their model could be used as a powerful tool for analyzing the spread impact of different dependence assumptions and parameter values.…”