We give an overview of a broad class of models designed to capture stochastic volatility in financial markets, with illustrations of the scope of application of these models to practical finance problems. In a broad sense, this model class includes GARCH, but we focus on a narrower set of...

Recent developments allow a nonparametric separation of the continuous sample path component and the jump component of realized volatility. The jump component has very different time series properties than the continuous component, and accounting for this allows improved forecasting of future...

We consider European calls and puts on an asset whose forward price F(t) obeys dF(t)=α(t)A(F)dW(t,) under the forward measure. By using singular perturbation techniques, we obtain explicit algebraic formulas for the implied volatility σB in terms of today's forward price F0 ≡ F(0), the...

We derive an estimator for Black-Scholes-Merton implied volatility that, when compared to the familiar Corrado & Miller [JBaF, 1996] estimator, has substantially higher approximation accuracy and extends over a wider region of moneyness.

The current financial crisis offers a unique opportunity to investigate the leading properties of market indicators in a stressed environment and their usefulness from a banking supervision perspective. One pool of relevant information that has been little explored in the empirical literature is...