In this paper we study the pricing of commodity swaptions in a Heath-Jarrow-Morton framework based on stochastic spot prices, interest rates and convenience yields. We develop a complementary framework for deriving approximations of swaption prices. In the class of Gaussian models the method...

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...

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...