A Risk-Neutral Stochastic Volatility Model
Yingzi Zhu and Marco Avellaneda

We construct a risk-neutral stochastic volatility model using no-arbitrage pricing principles. We then study the behavior of the implied volatility of options that are deep in and out of the money according  to this model. The motivation of this study is to show the difference  in the asymptotic behavior of the  probability distribution tails between the Black Scholes log-normal probability and the risk-neutral stochastic volatility model.
In the second part of the paper we further explore  this risk-neutral stochastic volatility  model by a  Monte Carlo study on the implied volatility curve (implied volatility as a function of the option strikes)  for near-the-money options. We study the behavior of this ``smile'' curve under different choices of  parameters for the model, and determine how the shape  and the skewness of the ``smile'' curve is affected by the volatility-of-volatility  (``V-vol'')  and the correlation between the underlying asset and  its volatility.