Explaining Credit Default Swap Spreads with the Equity Volatility and Jump Risks of Individual Firms

TLDR: In this article, the authors tried to explain the credit default swap (CDS) premium, using a novel approach to identify the volatility and jump risks of individual firms from high-frequency equity prices.

Abstract: This paper tries to explain the credit default swap (CDS) premium, using a novel approach to identify the volatility and jump risks of individual firms from high-frequency equity prices. Our empirical results suggest that the volatility risk alone predicts 50 percent of the variation in CDS spread levels, while the jump risk alone forecasts 19 percent. After controlling for credit ratings, macroeconomic conditions, and firms’ balance sheet information, we can explain 77 percent of the total variation. Moreover, the pricing effects of volatility and jump measures vary consistently across investmentgrade and high-yield entities. The estimated nonlinear effects of volatility and jump risks on credit spreads are in line with the implications from a calibrated structural model with stochastic volatility and jumps, although the challenge of simultaneously matching credit spreads and default probabilities remains.

Figures

Figure 1: Credit curves

Figure 4: CDS spreads and volatility risks by rating groups

Table 6: Robustness check: panel data estimation

Figure 3: Linkages from asset and equity values to credit spreads

Table 7: Regressions by rating groups

Table 2: Summary statistics: (upper left) sectoral distribution of sample entities; (upper right) distribution of credit spread observations by ratings; (lower left) firm-specific information; (lower right) macro-financial variables

Full text

BIS Working Papers
No 181
Explaining Credit Default
Swap Spreads with Equity
Volatility and Jump Risks of
Individual Firms
by Benjamin Yibin Zhang, Hao Zhou & Haibin Zhu
Monetary and Economic Department
September 2005
JEL Classification Numbers: G12, G13, C14
Keywords: Structural Model; Stochastic Volatility; Jumps; Credit
Spread; Credit Default Swap; Nonlinear Effect; High Frequency
Data

BIS Working Papers are written by members of the Monetary and Economic Department of the Bank
for International Settlements, and from time to time by other economists, and are published by the
Bank. The views expressed in them are those of their authors and not necessarily the views of the
BIS.
Copies of publications are available from:
Bank for International Settlements
Press & Communications
CH-4002 Basel, Switzerland
E-mail: publications@bis.org
Fax: +41 61 280 9100 and +41 61 280 8100
This publication is available on the BIS website (www.bis.org).
© Bank for International Settlements 2005. All rights reserved. Brief excerpts may be reproduced
or translated provided the source is cited.
ISSN 1020-0959 (print)
ISSN 1682-7678 (online)

Explaining Credit Default Swap Spreads with
Equity Volatility and Jump Risks of Individual
Firms
∗
Benjamin Yibin Zhang
†
Hao Zhou
‡
Haibin Zhu
§
First Draft: December 2004
This Version: September 2005
Abstract
A structural model with stochastic volatility and jumps implies particu-
lar relationships between observed equity returns and credit spreads. This
paper explores such effects in the credit default swap (CDS) market. We
use a novel approach to identify the realized jumps of individual equity
from high frequency data. Our empirical results suggest that volatility risk
alone predicts 50% of CDS spread variation, while jump risk alone forecasts
19%. After controlling for credit ratings, macroeconomic conditions, and
firms’ balance sheet information, we can explain 77% of the total variation.
Moreover, the marginal impacts of volatility and jump measures increase
dramatically from investment grade to high-yield entities. The estimated
nonlinear effects of volatility and jumps are in line with the model implied-
relationships between equity r eturns and cr edit spreads.
JEL Classification Numbers: G12, G13, C14.
Keywords: Structural Model; Stochastic Volatility; Jumps; Credit Spread;
Credit Default Swap; Nonlinear Effect; High Frequency Data.
∗
The views presented here are solely those of the authors and do not necessarily represent
those of Fitch Ratings, the Federal Reserve Board, or the Bank for International Settlements.
We thank Jeffrey Amato, Ren-Raw Chen, Greg Duffee, Mike Gibson, Jean Helwege, Jingzhi
Huang, and George Tauchen for detailed discussions. Comments from seminar participants at
the Federal Reserve Board, the 2005 FDIC Derivative Conference, the Bank for International
Settlements, and the 2005 Pacific Basin Conference at Rutgers are greatly appreciated.
†
Benjamin Yibin Zhang, Fitch Ratings, One State Street Plaza, New York, NY 10004, USA.
Tel.: 1-212-908-0201. Fax: 1-914-613-0948. E-mail: ben.zhang@fitchratings.com.
‡
Hao Zhou, Federal Reserve Board, Mail Stop 91, Washington, DC 20551, USA. Tel.: 1-202-
452-3360. Fax: 1-202-728-5887. E-mail: hao.zhou@frb.gov.
§
Haibin Zhu, Bank for International Settlements, Centralbahnplatz 2, 4002 Basel, Switzer-
land. Tel.: 41-61-280-9164. Fax: 41-61-280-9100. E-mail: haibin.zhu@bis.org.

Explaining Credit Default Swap Spreads with
Equity
Volatility and Jump Risks of Individual Firms
Abstract
A structural model with stochastic volatility and jumps implies particular rela-
tionships between observed equity returns and credit spreads. This paper explores
such effects in the credit default swap (CDS) market. We use a novel approach
to identify the realized jumps of individual equity from high frequency data. Our
empirical results suggest that volatility risk alone predicts 50% of CDS spread
variation, while jump risk alone forecasts 19%. After controlling for credit rat-
ings, macroeconomic conditions, and firms’ balance sheet information, we can
explain 77% of the total variation. Moreover, the marginal impacts of volatility
and jump measures increase dramatically from investment grade to high-yield en-
tities. The estimated nonlinear effects of volatility and jumps are in line with the
model-implied relationships between equity returns and credit spreads.
JEL Classification Numbers: G12, G13, C14.
Keywords: Structural Model; Stochastic Volatility; Jumps; Credit Spread; Credit
Default Swap; Nonlinear Effect; High Frequency Data.

Frequently asked questions

Q1. What are the contributions in "Explaining credit default swap spreads with equity volatility and jump risks of individual firms" ?

This paper explores such effects in the credit default swap ( CDS ) market. After controlling for credit ratings, macroeconomic conditions, and firms ’ balance sheet information, the authors can explain 77 % of the total variation. Their empirical results suggest that volatility risk alone predicts 50 % of CDS spread variation, while jump risk alone forecasts 19 %. 

Q2. What are the three major filtering criteria used to remove potential measurement errors?

8Three major filtering criteria are adopted to remove potential measurement errors: (1) an outlier criterion that removes quotes that are far above or below the average prices reported by other contributors; (2) a staleness criterion that removes contributed quotes that do not change for a very long period; and (3) a term structure criterion that removes flat curves from the dataset. 

Q3. How much of the variance is accounted for by the jump component?

In those days when significant jumps have been detected, the jump component contributes to 52.3% of the total realized variance on average (the range is around 40-80% across the 307 entities). 

Q4. What are the main criteria used to remove the spreads?

In addition, the authors also remove those CDS spreads that are higher than 20%, because they are often associated with absence of trading or a bilateral arrangement of an upfront payment. 

Q5. Why do the authors eliminate the subordinated class of contracts?

The authors eliminate the subordinated class of contracts because of their small relevance in the database and unappealing implication in credit risk pricing. 

Q6. What are the explanatory variables for the CDS spread?

Their explanatory variables include their measures of individual equity volatilities and jumps, rating information, and other standard structural factors including firm-specific balance sheet information and macro-financial variables. 

Q7. What are the common variables used to measure the volatility of a firm?

Following the prevalent practice in the existing literature, their firm-specific variables include the firm leverage ratio, return on equity (ROE), and dividend payout ratio. 

Q8. What are the advantages of CDS spreads?

Blanco et al. (2005) and Zhu (2004) show that, while CDS and bond spreads are quite in line with each other in the long run, in the short run CDS spreads tend to respond more quickly to changes in credit conditions. 

Q9. What are the two assumptions the authors have used in the identification process?

The infrequent occurrence and relative importance of the jump component validate the two assumptions the authors have used in the identification process. 

Q10. What are the four variables used to proxy for the overall state of the economy?

And to proxy for the overall state of the economy, the authors use four macro-financial variables: the S&P 500 average daily return and its volatility in the past 6 months, and the average 3-month Treasury rate and the slope of the yield curve in the previous month. 

Q11. What is the main reason why CDSs lead the bond market in price discovery?

The fact that CDSs lead the bond market in price discovery is instrumental for their improved explanation of the temporal changes in credit spread by default risk factors. 

Q12. How does the R-square increase after controlling for credit ratings?

After controlling for credit ratings, macro-financial variables, and firms’ accounting information, the signs and significance of jump and volatility impacts remain solid, and the R-square increases to 77%. 

Q13. What is the average daily return volatility?

The average daily return volatility (annualized) is between 40-50%, independent of whether historical or realized measures are used.