Term Structure of Volatility

[peter333]

Dear David:

I could not understand one LOS in your notes on Hull Chapter 16 on Volatility Smiles. Explain how the volatility term structure and volatility surfaces may be used to price options.

You have defined both the volatility term structure and volatility surfaces but it is not clear how they can be used to price options. An implication can be that term to maturity goes up, volatility goes up and option price goes up. But still it is unclear about volatility surfaces.

best

 

[David Harper CFA FRM]

Hi Peter,

You have a point for the first step. Normally we price, say, the call as function of inputs in BS:

c = F[S, K, vol, r, T]

Implied volatiliy "inverts;" goal-seeks to find the volatility that makes the model price = the market price. So, as a first step, to your point, you need a c in order to goal seek for the volatility:

what vol, if input into F[S, K, vol, r, T] gives a result of c that matches the market price of c.

Given a set of call prices, we can build the implied volatility surface; i.e., the implied vols at various strikes and terms. As a build, it will be a collection of points. Via interpolation/curve fitting/etc, the surface is constructed.

Then, as a second step, now this volatility surface can be used to price *other* options, including options were we don't have market prices. For those, we can "lookup" the volatility to be used as in input to price them. Or, it can be used to adjust our historical vol to account for smile/skew. So, it's sort of a two-step...

David

 

[peter333]

Thanks David...I hope I will be able to nail such questions down now .