Credit-implied forward volatility and volatility expectations

We show how one can back out implied forward volatility term structures from credit default swap spreads. Such forward stock volatility term structures are useful for instance in forward start option pricing. We find the term structure to be downward-sloping, and the credit market's volatility forecasts tend to vary more across time than across maturities. Long-term volatility expectations, in turn, are found to be low and stable while short-term expectations are higher and more volatile. The volatility expectation's mean-reversion rate, finally, indicates that the credit market expects volatility shocks in the equity market to last for several years.