# Presentation: 677121

## 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.