Most option pricing models assume all parameters except volatility are fixed; yet they almost invariably change on re‐calibration. This article explains how to capture the model risk that arises when parameters that are assumed constant have calibrated values that change over time and how to use...

A price process is scale-invariant if and only if the returns distribution is independent of the price level. We show that scale invariance preserves the homogeneity of a pay-off function throughout the life of the claim and hence prove that standard price hedge ratios for a wide class of...

We derive the local volatility hedge ratios that are consistent with a stochastic instantaneous volatility and show that this ‘stochastic local volatility’ model is equivalent to the market model for implied volatilities. We also show that a common feature of all Markovian single factor...

This paper examines the ability of several different continuous-time one and two-factor jump-diffusion models to capture the dynamics of the VIX volatility index for the period between 1990 and 2010. For the one-factor models we study affine and non-affine specifications, possibly augmented with...

This paper examines the ability of twelve different continuous-time two-factor models with mean-reverting stochastic volatility to capture the dynamics of the S&P 500 and three European equity indices. The stochastic volatility models are the square root variance, GARCH, and log volatility...

This paper implements a variety of different calibration methods applied to the Heston model and examines their effect on the performance of standard and minimum-variance hedging of vanilla options on the FTSE 100 index. Simple adjustments to the Black-Scholes-Merton model are used as a...

This paper examines the ability of several different continuous-time one- and two-factor jump-diffusion models to capture the dynamics of the VIX volatility index for the period between 1990 and 2010. For the one-factor models we study affine and non-affine specifications, possibly augmented...

This paper investigates the determinants of the iTraxx CDS Europe indices, finding strong evidence that they are regime dependent. During volatile periods credit spreads become highly sensitive to stock volatility and more sensitive to this than to stock returns. They are also almost immune to...