We consider general stochastic volatility models with no local volatility component and derive the general expression of the volatility smile at order two in volatility-of-volatility. We show how, at this order, the smile only depends on three dimensionless numbers whose precise expressions as...

This is Chapter 2 of Stochastic Volatility Modeling, published by CRC/Chapman & Hall.In this chapter the local volatility model is surveyed as a market model for the underlying together with its associated vanilla options.First, relationships of implied to local volatilities are derived, as well...

We begin by deriving suitability conditions for risk-management models for derivatives and review the Black-Scholes model. Next, the (in)efficiency of delta-hedging is analyzed by quantifying the standard deviation of the carry P&L of a delta-hedged position in the Black-Scholes case and in the...

In this paper we address the relationship between the smile that stochastic volatility models produce and the dynamics they generate for implied volatilities. We introduce a new quantity, which we call the Skew Stickiness Ratio and show how, at order one in the volatility of volatility, it is...

In two previous articles, we assessed the structural limitations of existing models for equity derivatives and introduced a new model based on the direct modelling of the joint dynamics of the spot and the implied variance swap volatilities. Here we present new work on an extension of this model...

In a previous article we highlighted how traditional stochastic volatility and Jump/Lévy models impose structural constraints on how the short forward skew, the spot/vol correlation, and the term structure of the vol-of-vol are related. Here we propose a model that enables them to be controlled...

Traditionally smile models have been assessed according to how well they fit market option prices across strikes and maturities. However, the pricing of most of the recent exotic structures, such as reverse cliquets or Napoleons, is more dependent on the assumptions made for the future dynamics...

When designing multi-asset stochastic volatility (SV) or local-stochastic volatility (LSV) models, one of the main issues involves the construction of the global correlation matrix. Typically correlation matrices for each assets' degrees of freedom are set and the challenge is to build a global...