# How to price a volatility-index option?

There exist several volatility indices, such as the CBOE Volatility Index (VIX). There are also options on such indicies.

What is the best way to price a volatility-index option? Is there a simple model that works well in terms of performance and precision?

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You can price a VIX option by looking at the volatility of the volatility. This is called vomma: en.wikipedia.org/wiki/Greeks_%28finance%29#Vomma (this doesn't answer your question, but might be trivially helpful) –  barrycarter Oct 10 '11 at 2:47

Volatility and variance derivatives, such as the VIX, are priced by creating a replicating portfolio of options, weighted so as to have constant gamma for a wide range price levels. So an option on such a structure would necessarily be the sum of options on each of the individual options in the replicating portfolio. Thus, the question of their pricing reduces to the question of pricing options on options, which is easier to research. Or is the question how you price an option on an option?

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Hi Jason, welcome to quant.SE and thanks for contributing your answer. However, I think you are incorrect. The VIX methodology actually takes the square root of the price of a replicating portfolio of options. Hence a VIX option is an option on the square root of prices of a portfolio of a bunch of other options. This is a different and presumably more difficult problem than pricing options on options. –  Tal Fishman Sep 19 '11 at 14:55
Oh the VIX is a volatility swap? I thought it was a variance swap. So I guess any option-option model would have to be adapted to consider the square root of the assumed process -- that does sound pretty nontrivial. That said, it seems like you could do it pretty easily by adopting Monte Carlo integration as your solution approach. –  Jason Sep 19 '11 at 15:40