This study extends the literature on the relation between trading activity and volatility by looking at a new asset class in the form of VIX futures, and by decomposing each side of the relation into two components. The results confirm several findings documented in prior studies: The number of...

We examine the effects from the Trading At Settlement (TAS) introduction on VIX futures market quality. We find that the VIX futures market exhibits higher trading activity and better liquidity after the TAS introduction. VIX futures traders use the TAS limit order book to execute large...

This paper suggests a stochastic volatility term-structure model applied to the pricing of electricity swaptions in the Nordic power market traded at the Nasdaq OMX Commodities exchange. The volatility structure in the model is specified as a product of a time-dependent function that handles the...

In this paper we examine the empirical performance of affine jump diffusion models with stochastic volatility in a time series study of crude oil prices. We compare four different models and estimate them using the Markov Chain Monte Carlo method. The support for a stochastic volatility model...

This study investigates volatility spillovers to electric power from large exogenous shocks in the prices of gas, coal, and carbon emission allowances in the German energy market. Our sample ranges from 2008 to 2016 and covers periods of different market conditions. We use a general VAR-BEKK...

In this paper we develop a general method for deriving closed form approximations of European option prices and equivalent implied volatilities in stochastic volatility models. Our method relies on perturbations of the model dynamics and we show how the expansion terms can be calculated using...

In this paper we derive closed form approximations of European option prices in different versions of the SABR model of Hagan et al. (2002). Our approach is based on perturbing the model dynamics and approximations of call prices are obtained from a second order Taylor expansion. The method is...