Some recent specifications for GARCH error processes explicitly assume a conditional variance that is generated by a mixture of normal components, albeit with some parameter restrictions. This paper analyses the general normal mixture GARCH(1,1) model which can capture time-variation in both...

Current research on financial risk management applications of econometrics centres on the accurate assessment of individual market and credit risks with relatively little theoretical or applied econometric research on other types of risk, aggregation risk, data incompleteness and optimal risk...

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...

This paper formalizes the class of scale-invariant volatility models and explores its hedging properties. A model is 'scale-invariant' if and only if its probability distribution of asset returns is independent of the current level of the asset price. We provide a set of equivalent properties...

The delta hedging performance of deterministic local volatility models is poor, with most studies showing that even the simple constant volatility Black-Scholes model performs better. But when the local volatility model is extended to capture stochastic dynamics for the spot volatility process,...

There are two unique volatility surfaces associated with any arbitrage-free set of standard European option prices, the implied volatility surface and the local volatility surface. Several papers have discussed the stochastic differential equations for implied volatilities that are consistent...

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...