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mathdude2018
Topic Author
Posts: 15
Joined: January 10th, 2018, 4:35 pm

Creating volatility term structure

February 19th, 2020, 11:04 pm

I am trying to understand how to create volatility term structure if I know volatility at certain point in time. 

I have only 1 known volatility of 40% exactly 90 days from now. How do I create an equivalent volatility for 120 days, 180 days, 200 days, etc. Is there a more rigorous way than to use sigma * sqrt(T) ?
 
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lePiddu
Posts: 15
Joined: March 17th, 2015, 2:15 pm

Re: Creating volatility term structure

February 20th, 2020, 5:01 pm

Is this volatility the "thing" you want to use as argument of BlackScholes / Black / Bachelier formulas for option pricing? Implied volatility term structures are often a bit different from those estimated from historical data.

Anyway what you need is a time series model with some dynamics for the volatility (typical choice is some conditionally heteroskedastic models GARCH-style). Once you have estimated your parameters for the volatility dynamic you can forecast the variance (expected) value over some future period of time. You integrate this forecasted series over the period (you can do it numerically) and then take the Square root and annualize the value. Boom you got your "volatility" up to the final forecasting time.

You can move your forecasting horizon and create a nice term structure.

I can suggest you the evergreen John Hull's book Options Futures and other derivatives. In the tenth edition is chapter 23.
 
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fomisha
Posts: 29
Joined: December 30th, 2003, 4:28 pm

Re: Creating volatility term structure

February 21st, 2020, 12:14 am

What's the definition of "equivalent volatility"?
What are you trying to achieve?