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How Important Is Option-Implied Volatility for Pricing Credit Default Swaps?

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?.

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How Important Is Option-Implied Volatility for Pricing Credit Default Swaps?

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  1. 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

  2. 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.

  3. 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?

  4. 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.

  5. 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.”

  6. 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?

  7. 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

  8. Credit GradesStructural 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.

  9. Credit GradesStructural 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.

  10. 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.

  11. 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?

  12. 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.

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