How Important Is Option-Implied Volatility for Pricing Credit Default Swaps? By Charles Cao, Fan Yu, Zhaodong Zhong Comments by Dan Nuxoll 27 October 2006

Why Volatility? Structural models following Merton (1974) postulate that the likelihood of default is closely related to the volatility of a firm’s assets. Firms with more volatile assets tend to default more. Because CDS are protection against defaults, default rates are the critical inputs to CDS spreads. Ergo, structural models imply that volatility should be closely related to CDS spreads.

Inferred vs. Realized Volatility Two Available Measures of Volatility –Realized Stock Price Volatility –Inferred Volatility from Stock Options Prices Higher volatility increase the value of options because they are more likely to be exercised. Which works better in forecasting CDS spreads? –Inferred volatility is forward-looking, realized volatility is backward-looking. –Inferred volatility also includes a risk premium that can change even if expected volatility does not change. –Finally, how liquid are stock options?

Which Volatility? Which historical volatility? –Most of the work is done with 252-day volatility. –Other horizons are tested as well: 22, 63, 126, and 1000 days. –No exponentially weighted or GARCH volatilities.

Which Volatility? Which implied volatility? –Equity options with different strike prices and maturities have different implied volatilities. –Solution: volatility constructed to “minimize the sum of squared pricing errors across all put option with nonzero open interest each day…” –Is this number a good summary of the entire volatility surface? –But “we find that [the standardized implied volatilities] can be quite sensitive to the discrete maturity and moneyness effects.”

Two Exercises Regression Horserace Which is more closely related to CDS spreads? Credit Grades—a structural model of pricing CDS Which performs better in a pricing model?

Regression Horserace Firm-by-firm regressions –Independent variable: CDS spread observations. –Dependent variable: various control variables and the two measures of volatility. –Implied volatility has larger and more significant coefficients. –Especially for firms for which CDS spreads are especially volatile. with very active options markets with poor credit ratings

Credit Grades Structural model of CDS spreads Evidence not as persuasive –Pricing errors are relatively high Average CDS spread is 152 bp; median is 83 bp. Average pricing error for implied volatility is -15 bp; RMSE is 59 bp. –For some the samples with less volatile CDS spreads, historical volatility does better. –Nonetheless, implied volatility is better for: for the sample as a whole; for the sample with the most volatile CDS spreads; for firms with poor ratings; for firms for which there is a large open interest. –Not clear if the problem is the model, the three estimated nuisance parameters, or measures of volatility.

Credit Grades Structural model of CDS spreads Results are robust to the different horizons for measuring historical volatility: 22 days to 1000 days. Intriguing result: –The 1000 day measure does best by some measures (e.g. RMSE of the pricing model). –The 126 day measure also does well. –The 22 day measure is clearly the worst.

Intriguing Experiment Because of risk premia, implied volatility is a biased forecast of future volatility. (This result is confirmed.) CDS spreads are regressed on: –future volatility (pure volatility??); –the difference between implied volatility and future volatility (pure risk premia??). Both are significant.

Intriguing Experiment Suggestion: –Instead use a forecast of volatility –and the difference between the implied volatility and the forecast volatility. –Three forecasting models are available in Table 13. Is it possible to use information from the portfolio to identify changes in market risk premia?

A Question The authors concentrate on 5-year CDS. What is the appropriate volatility for defaults over a five-year horizon? Approximately 80% of the contracts used in this paper mature in less than 180 days. Approximately 80% of the contracts have strike prices greater than 80% of the current price.