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...

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...

We model investment opportunities with a single source of uncertainty, i.e. the market price of the investment. Investment cost can be predetermined or perfectly correlated with the market price. The common paradigm for risk-neutral real-option pricing is a special case en- compassed within our...

Most banks employ historical simulation for Value-at-Risk (VaR) calculations, where VaR is computed from a lower quantile of a forecast distribution for the portfolio’s profit and loss (P&L) that is constructed from a single, multivariate historical sample on the portfolio’s risk factors....