Predicting credit default swap prices with financial and pure data-driven approaches

Abstract

The increasing popularity of credit default swaps (CDSs) necessitates understanding their various features. In this study, we analyse the capability of CDSs in predicting CDS prices of other companies in the same risk class or CDS prices of further time horizons. In doing so, we employ the basic forms of structural (the Merton model) and reduced-form (constant intensity) models in a cross-sectional and a time series setup. By utilizing a credit default swap dataset exclusively for estimation and out-of-sample prediction, our study also serves as a comparison between the basic forms of credit risk models. Finally, it contrasts the results with the performance of a new supervised learning forecasting technique, the Support Vector Machines Regression. We show that although the Merton and the constant intensity models handle default timing and interest rates differently, the prediction performance in cross-sectional and time series analyses is, on average, similar. In one-, five-, and 10-step-ahead predictions of time series, the machine learning algorithm significantly outperforms financial models.

Keywords:

• Credit risk
• Credit default swaps
• Credit derivatives
• Support Vector Machines Regression
• Structural credit risk models
• Reduced-form credit risk models

Acknowledgements

We are grateful to the German Research Foundation (DFG) for financial support through the Information Management and Market Engineering Program at Karlsruhe Institute of Technology. Earlier versions of this paper were presented at French Finance Association Annual Meetings 2006, Poitiers, Eastern Finance Association Meetings 2007, New Orleans, Financial Management Association European Meetings 2007, Barcelona, and European Financial Management Association Meetings 2007, Vienna.

Notes

§Since the beginning of the financial crisis in 2007, the CDS market has been especially affected. Among the lessons learned from the crisis is the need to strengthen market infrastructures for credit default swaps, thereby recognizing the importance of CDS markets for overall financial stability.

†In addition, there is a related literature focusing on actual default probabilities. See, for example, Leland (2004) and Denzler et al. (2006). In contrast to our line of research, there is also a literature that aims at explaining bond or CDS spreads with economical factors (Collin-Dufresne et al. 2001, Ericsson et al. 2009).

†These include Jones et al. (1984), Ogden (1987), Eom et al. (2004), Ericsson and Reneby (2004), Bakshi et al. (2006) and Frühwirth and Sögner (2006).

‡See Houweling and Vorst (2005).

§Longstaff et al. (2005). The study also incorporates bond data in the estimation process for the liquidity premium.

¶In contrast, securities like bonds are in fixed supply. For a thorough discussion, see Longstaff et al. (2005).

†Although weekday effects on bond prices are well documented (Flannery and Protopapadakis 1988, Johnston et al. 1991, Frühwirth et al. 2010), we have no evidence that they play a major role in the CDS market.

‡Usage of actual transaction data would result in a rather small dataset with inferior time series. In order to pursue an empirical study with abundant data, the indicative prices are utilized.

§For a more in-depth study on the microstructure effects on credit default swap prices, Gündüz et al. (2007) analyses the choice of trading venues with the same dataset.

¶Similar results have been reached by other studies. See Gündüz et al. (2007) for a detailed discussion on regional CDS pricing differences.

†See findings of Frühwirth and Sögner (2003, 2006) and Houweling and Vorst (2005).

‡Although the 0.5 figure is derived from the US market, recent efforts with European data have also relied on this figure (Houweling and Vorst 2005, Frühwirth and Sögner 2006). Considering the fact that Basle 2 provisions accept a loss given default of 50% for bank loans independent of the country chosen, this is not an unrealistic assumption.

†Without the use of kernels, the problem of nonlinear machine construction would have required two steps. First, a fixed nonlinear mapping to transform the data into a ‘feature’ space where the analysis is easier, and then a linear machine to classify/regress it in the feature space. Kernel theory stipulates that an inner product in feature space has an equivalent kernel in input space; utilizing kernel functions therefore simplifies the algorithm. There is no longer the need to think about the mapping and evaluation of the feature map, but only about the inner products of the test and training variables (for details, see Gunn 1998 and Cristianini and Shawe-Taylor 2000).

‡Cao and Tay (2001) have shown that the generalization error is not greatly influenced by parameter C. In their study, the errors change only slightly when C is increased from 0.0001 to 1000. In parallel, in the study of Tay and Cao (2001), an appropriate choice for C is mentioned to be between 10 and 100. Similarly, they report the small impact of the selection of the ϵ-insensitive band.

†Minimizing the sum of squared differences was a possible alternative, which would have simply returned the default probability for the average of s ^obs on any given day. The results from using this approach do not differ significantly.

‡The authors utilized a period between January 1999 and July 2000. In their estimates, A-rated banks had a lower average intensity than Aa-rated banks, which should supposedly be higher.

†The traditional approach for estimating asset value and asset volatility is based on Jones et al.'s (1984) study. Here, the asset value is estimated as the sum of traded debt, non-traded debt and equity value. After an initial estimate for asset volatility is reached from the returns on asset value, this is refined through an equality reached from Ito's Lemma, which formulates asset volatility as a function of equity volatility. Alternative versions of this approach are followed by Anderson and Sunderasan (2000), Lyden and Saraniti (2000) and Eom et al. (2004). Ronn and Verma (1986) extended Jones et al.'s (1984) single equation to solve two simultaneous equations for two unknowns, asset value and volatility, where the second equation is simply used to view equity as the call option on the asset value. A completely different alternative has arisen from the work of Duan (1994), who introduced an ML approach, proponed by Ericsson and Reneby (2004, 2005), with good prediction results. Overall, the estimation technique for structural models remains an open research question in the field.

†There are 2650 data points in the training input and output sets from the data of five companies for each set, respectively; 2120 data points in test input and output sets were used from the data of four companies for each set.

†Only consecutive 14-day periods of observation were used to ensure the continuity of the time series. The estimation sample is simply 14 more for each firm in the risk class and has not been explicitly tabulated.

†The five-day- and 10-day-ahead prediction errors are also significantly better than the financial models, which have not been tabulated.