We study the term structure of the implied volatility in a situation where the smile is symmetric. Starting from the result by Tehranchi that a symmetric smile generated by a continuous martingale necessarily comes from a mixture of normal distributions, we derive representation formulae for the...

In this paper, we focus on short-time asymptotics for American options in the case of local and stochastic volatility models. As a by-product, we obtain an efficient algorithm for calibrating Dupire's local volatility to American options, starting from an arbitrage-free parametrization of a...