Feb
14

## Stochastic Volatility Models and the Pricing of VIX Options

**Stochastic Volatility Models and the Pricing of VIX Options**is written by Joanna Goard, Mathew Mazur and published in Mathematical Finance. It examines and compares the performance of several volatility models to estimate the VIX, a measure of the implied volatility of S&P 500 index options. You can get access to the paper here.

An accurate estimation of VIX is obviously important given its special role as the fear gauge, there is extensive literature trying to do so, among them, mean-reverting models are especially popular. The authors compare eight different mean-reverting models, with each having different mean reversion speed or diffusion term, specifically, they can be summarized as follows in table 2.1:

Using VIX index values between 1990 and 2009, the authors estimate parameters of the eight models by generalized method of moments (GMM) approach, and calculate the root mean squared error (RMSE),

where equation (1) and (2) are two measures of error term.

**Model 7 (3/2 model with quad drift)**has the best performance among the eights.

Another big contribution of this study is the authors derive a closed form solution for a European call option under Model 7. The option pricing performance of model 7 outperforms other candidates as well.

What's nice of the

**Model 7 (3/2 model with quad drift)**is its parsimony, it has only three parameters same as Cox–Ingersoll–Ross model (CIR).

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