Derman, Implied and local volatility, etc

Discussion in 'Options' started by Grant, Nov 11, 2006.

  1. Grant


    Perhaps someone can clarify a few points for me re Emanuel Derman’s paper, “Modeling the Volatility Smile” ,October 2006

    Generally, how is the volatility of volatility determined (I can determine implied by iteration)?

    How do I reconcile these statements (page 6):”Volatility of Implied Volatility Decreases with Expiration” and “Short-term implied volatilities are more volatile”? Presumably, (short-term, reducing ) volatility of implied is derived from (short-term, more volatile) implieds?

    Continuing from above: “This suggests mean reversion or stationarity …”. ”Stationarity” is not in my English dictionary (probably in an American). Does this mean stationary? If so, which is it – mean reverting or stationary? Or have quants embraced aspect of quantum physics, now?

    Continuing from the points above (page 13): “as assets approach liabilities, equity volatility increases”. I’m assuming here “assets” could refer to the underlying and “liabilities” refers to strikes. Again, this appears to conflict with ”Volatility of Implied Volatility Decreases with Expiration” assuming underlying volatility necessarily transfers to its derivatives.

    The Quantitative Strategies Research Notes he jointly produced while at Goldman Sachs are models of clarity and lucidity for the mathematically challenged (myself). Don’t know what happened with this one.

    Any help greatly appreciated. Thank you in advance.

  2. (1) You might get "better" answers at (2) I tended to believe that shorter-dated options are dominated by theta, delta and gamma while longer-dated options are dominated by vega. Short-dated options behave more like their underlying instead of being more option-like. (3) The statement pertaining to shorter-term volatilities being more volatile I don't take too seriously. Again, the delta, gamma and theta dominate the value of the option. (4) Regarding the vol of the vol, maybe it can be related to the slope of the skew. Steeper skews have greater vol movement. Flat skews have stationary/stagnant vol. I hope that helps.
  3. Grant



    Thank you for the reply.

    I can look at your points in my model. Hopefully this will then demonstrate what Derman refers to. Seems more straightforward in your terms.

    Thanks, once again.