Local volatility models

Expanded smiles

Implementing models with stochastic as well as deterministic local volatility can be challenging. Here, Jesper Andreasen and Brian Huge describe an expansion approach for such models that avoids the high-dimensional partial differential equations usually…

A dynamic model for correlation

Equity markets have experienced a significant increase in correlation during the crisis, resulting in exotic derivatives portfolios realising large losses. As larger correlations in downward scenarios are already implied in the index option market in the…

Smile dynamics II

In an article published in Risk in September 2004, Lorenzo Bergomi highlighted how traditionalstochastic volatility and jump/Lévy models impose structural constraints on the relationshipbetween the forward skew, the spot/volatility correlation and the…

An arbitrage-free interpolation of volatilities

Nabil Kahalé describes a new construction of an implied volatilities surface from a discrete set of implied volatilities that is arbitrage-free and satisfies some smoothness conditions. His method provides an excellent fit to the smile of the local…

Universal Barriers

As our survey in this issue shows, there is an increasing volume of barrier products traded in the forex options market. Here, Alexander Lipton and William McGhee discuss the pricing of barriers under various model frameworks, with particular focus on…