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...

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...

The assumption that the probability distribution of returns is independent of the current level of the asset price is an intuitive property for option pricing models on financial assets. This ‘scale invariance’ feature is common to the Black-Scholes (1973) model, most stochastic volatility...

Different theoretical and numerical methods for calculating the fair-value of a variance swap give rise to systematic biases that are most pronounced during volatile periods. For instance, differences of 10-20 percentage points would have been observed on fair-value index variance swap rates...

Most research on option hedging has compared the performance of delta hedges derived from different stochastic volatility models with Black-Scholes-Merton (BSM) deltas, and in particular with the `implied BSM’ model in which an option’s delta is based on its own market implied volatility....

Conditional returns distributions generated by a GARCH process, which are important for many problems in market risk assessment and portfolio optimization, are typically generated via simulation. This paper extends previous research on analytic moments of GARCH returns distributions in several...

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...

A comprehensive description of the trading and statistical characteristics of VIX futures and their exchange-traded notes motivates our study of their benefits to equity investors seeking to diversify their exposure. We analyze when diversification into VIX futures is ex-ante optimal for...

This paper introduces a new class of generalized beta-generated distributions that have very flexible shapes and tractable properties. Their quantiles and moments have a simple closed form and they are maximum entropy distributions under three simple conditions. Two special cases are the...