We develop a simple robust method to distinguish the presence of continuous and discontinuous components in the price of an asset underlying options. Our method examines the prices of at-the-money and out-of-the-money options as the option's time-to-maturity approaches zero. We show that these...

This paper develops static hedges for several exotic options using standard options. The method relies on a relationship between European puts and calls with different strike prices. The analysis allows for constant volatility or for volatility smiles or frowns. Copyright The American Finance...

We document a surprising pattern in S&P 500 option prices. When implied volatilities are graphed against a standard measure of moneyness, the implied volatility smirk does not flatten out as maturity increases up to the observable horizon of two years. This behavior contrasts sharply with the...

Using 3 years of interest rate caps price data, we provide a comprehensive documentation of volatility smiles in the caps market. To capture the volatility smiles, we develop a multifactor term structure model with stochastic volatility and jumps that yields a closed-form formula for cap prices....