The parametric estimation of stochastic differential equations (SDEs) has been the subject of intense studies already … mathematics for the dynamics of asset prices and their volatility. Calibrating it to real data would be very useful in many … practical scenarios. It is very challenging, however, since the volatility is not directly observable. In this paper, a complete …

In a tractable stochastic volatility model, we identify the price of the smile as the price of the unspanned risks … traded in SPX option markets. The price of the smile reflects two persistent volatility and skewness risks, which imply a …-form and structural models of stochastic volatility …