Pricing of risk in the long run with strong persistence in volatility

The credit spread and credit default swap (CDS) price are prices of risk in two markets. If the markets price risk equally in the long run, the prices should be equal. The non-arbitrage relation is tested as an equilibrium relation in the cointegrated vector autoregressive (VAR) model. Empirical studies typically find that the prices are cointegrated for some but not all companies in a sample. Some theoretical reasons for rejecting cointegration between CDS prices and credit spreads are discussed in the finance literature. However, there are several issues related to the time series properties of the series. For a sample of ten large companies and daily data from 2009 to 2016, we show that there is strong persistence in the series, strong persistence in volatility, and the errors are skewed and heavy-tailed. The existence of fourth moments of the errors is not satisfied for some of the companies. Asymptotic and bootstrap tests become unreliable in the presence of conditional heteroskedasticity. Monte Carlo simulations show that wild bootstrap tests have size close to the nominal level even when the existence of fourth moments is not satisfied. The power of wild bootstrap tests is low. Obtaining high power requires time series of more than 1000 observations or more than four years of daily observations.