is volatility term structure of S&P500 options decreasing or increasing over maturities?

sabrinalee · November 27th, 2011, 3:12 pm

I saw some places say B-S implied volatility increases with longer days to maturity under a certain strike price/moneyness. However, I also saw other places report a decreasing function. Can anyone explain to me if it is increasing or decreasing over days to maturity? or maybe the answer is mixed like sometimes increasing and sometimes decreasing? Thank you very much for your information.

bwarren · November 27th, 2011, 3:40 pm

There's no rule that says the term structure of volatility has to be increasing or decreasing, although the total variance must be nondecreasing. The skew tends to flatten out as you go to longer maturities, so in general, the vol term structure will be decreasing for lower strikes and increasing for higher ones.

sabrinalee · November 27th, 2011, 3:49 pm

Thank you very much for your response. I computed the average BS implied vol for each moneyness category (ITM, ATM, OTM) for different range of maturities. I find weird results that the term structure is increase when is or close to ATM, decreasing for OTM, increasing for slight ITM and flat for deeper ITM. It is for S&P500 index.