Practical problems with tests of cointegration rank with strong persistence and heavy-tailed errors: An application to the pricing of risk in the long run

Niklas Ahlgren, Paul Catani

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

Abstract

The price of a credit default swap (CDS) and the bond spread are two market
prices of risk. If the two markets price credit risk equally in the long
run, there exists an approximate non-arbitrage relation between the CDS
price and bond spread. The parity condition can be tested as an equilibrium
relation in the cointegrated vector autoregressive (VAR) model. Empirical
studies have found that the CDS price and bond spread of US and European
investment-grade firms are cointegrated for some but not all firms in the
sample. Theoretical explanations for rejecting cointegration between the CDS
price and bond spread are suggested in the literature. In this paper we
consider empirical issues with tests of cointegration between CDS prices and
bond spreads in the heteroskedastic VAR model. Strong persistence and very
high persistence in volatility are stylised features of cointegrated systems
of CDS prices and bond spreads. We show that tests of cointegration rank
have low power under such conditions. One result from the power analysis is
that obtaining high power requires more than 1000 observations, or more than
four years of daily observations. Besides, there is empirical support that
the distribution of the errors is heavy-tailed with infinite fourth moment.
The asymptotic and bootstrap tests are invalid if the errors are
heavy-tailed with infinite fourth moment. Monte Carlo simulations indicate
that the wild bootstrap (WB) test may be justified with heavy-tailed errors
which do not have finite fourth moment. We apply the WB test to daily
observations from 2010 to 2016 on the CDS price and bond spread of US and
European investment-grade firms. The WB test accepts cointegration for most
firms in the full sample period. The evidence for cointegration is weak in
sub-sample periods from 2010 to 2013 and 2013 to 2016. Restrictions implied
by the theory are rejected for the companies with the strongest evidence for
cointegration. Our empirical results only partially support equal pricing of
risk in the CDS market and bond market.
Original languageEnglish
Title of host publication9th Nordic Econometric Meeting, May 24-27, 2017 in Tartu, Estonia
Number of pages32
Publication date2017
Publication statusPublished - 2017
MoE publication typeA4 Article in conference proceedings
Event9th Nordic Econometric Meeting (NEM) - Tartu, Tartu, Estonia
Duration: 24.05.201727.05.2017
Conference number: 9

Keywords

  • 511 Economics
  • Cointegration
  • Credit risk
  • Heavy tails
  • Conditional heteroskedasticity

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