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.