Jul 25

Credit default swap (CDS) spread determinants (academic papers)

by David Harper, CFA, FRM, CIPM

FRM |

Two interesting papers on CDS spread: The Credit Default Swap Market's Determinants  by Caitlin Ann Greatrex and The Complete Picture of Credit Default Swap Spreads - A Quantile Regression Approach by Pedro Pires.

Using Hull's procedure, in the FRM, we solve for the CDS spread that makes the net present value of the CDS transaction equal to zero at inception (expected payments by the "insured" should equal expected payoff by the "insurer." At least initially): as Greatrex writes, "The [CDS ] premium reflects both the probability of default and the loss given default and ‘equates the present value of premium payments to the present value of expected losses' (Morgan Stanley, p. 11)."

Professor Greatrex tests the ability of variables implied by structural approach (i.e., the Merton-type approach that gives PD as a function of firm value and firm asset volatility) to explain changes in CDS spread. She finds these can explain 30% of the variation in CDS spread changes:

  • Firm value (proxy = equity returns). This is the structural idea: higher firm value implies it is less likely that firm value will breach the default threshold in the future
  • Leverage (proxy = book value of debt/approximate enterprise value). Similarly structural; i.e., higher leverage implies future default is more likely
  • Volatility: in the Merton model, equity is a call option on firm's assets. This is a good application of the Stulz reading. What happens if firm volatility increases? The value of equity (the call option) goes up. Given a firm value, then, the value of debt must fall with increasing volatility [firm value = debt + equity]. Ergo, higher volatility implies an increase in the CDS spread.
  • Business climate (proxy: mean CDS spread on a certain for all firms in the same rating category as the individual firm)
  • Interest rates: also structural approach. We know this from Stulz' formula for credit spread: credit spread = –(1/T)LN(D/F) – interest rate. The higher the interest rate, the lower the implied credit spread.

Professor Pires et al similarly study the determinants of CDS spread. Their explanatory variables include:

  • Implied volatility
  • Put skew: this is a key adjustment to the problem of assuming normality in the structural approach. Specifically, the lognormal distribution in the Black-Scholes will underestimate the probability of a large jump (the model is skinny-tailed, the actual is fat-tailed) which, on the downside, results in default. The authors note, "Furthermore, buying (selling) a firm's very deep-out-of-the-money put option is very similar to selling (buying) the firm's subordinated debt. This fact suggests that CDS prices should embed information available in the volatility  skew."
  • Stock return (same as firm value above)
  • Historical volatility
  • Absolute (dollar) CDS bid-ask spread: this is the author's innovation, to include a factor to capture liquidity. Clearly, liquidity plays a role. The authors say, "Single name credit derivatives are generally traded over-the-counter and the market is relatively young. Hence, liquidity is expected to play a central role in the market. Being an OTC and non-continuous market, inventory and  search costs are especially significant and this is expected to be reflected in the CDS bid-ask spread." Further, they smartly use absolute rather then relative spreads, as CDS spreads are naturally normalized.

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