The 1987 market crash was associated with a dramatic and permanent steepening of the implied volatility curve for equity index options, despite minimal changes in aggregate consumption. We explain these events within a general equilibrium framework in which expected endowment growth and economic...

The long memory characteristic of financial market volatility is well documentedand has important implications for volatility forecasting and optionpricing. When fitted to the same data, different volatility models calculate theunconditional variance differently and could have very different...

This paper studies modelling and existence issues for market models of option prices in a continuous-time framework with one stock, one bond and a family of European call options for one fixed maturity and all strikes. After arguing that (classical) implied volatilities are ill-suited for...

The main result of the paper is a formula for zero time-to-maturity limit ofimplied volatilities of European options under a broad class of stochastic volatilitymodels. Based on this formula, we propose a closed-form approximation of theimplied volatility smile.[...]