We examine convenience yields in the EU-wide CO2 emissions trading scheme (EU-ETS) during the first Kyoto commitment period (2008-2012). We find that the market has changed from initial backwardation to contango with significantly negative convenience yields in futures contracts. We further...

Due to the well known fact that market returns are not normally distributed, we use generalized hyperbolic distributions for pricing options in a randomized discrete-time setup. The obtained formulas can be used for pricing options on stock indexes, currencies and futures contracts. We test them...

This work discusses potential pitfalls of applying linear regression models to explaining the relationship between spot and futures prices in electricity markets. We briefly introduce the theory for the analysis of the spot-futures price relationship and highlight selected issues of multiple...

In this paper we concentrate on power producers’ strategies on the electricity market with contracts and Asian-type call options for power delivery. We propose stochastic asymmetric supply function equilibrium and Cournot models that are based on the assumption of the stochastic behavior of...

The purpose of this paper is to show that using the toolkit of interest rate theory, already well known in financial engineering as the HJM model [D. Heath, R. Jarrow, A. Morton, Econometrica 60, 77 (1992)], it is possible to derive explicite option pricing formula and calibrate the theoretical...

The earliest model of stock prices based on Brownian diffusion is the Bachelier model. In this paper we propose an extension of the Bachelier model, which reflects the subdiffusive nature of the underlying asset dynamics. The subdiffusive property is manifested by the random (infinitely...

In this paper we discuss subdiffusive mechanism for the description of some stock markets. We analyse the fractional Black–Scholes model in which the price of the underlying instrument evolves according to the subdiffusive geometric Brownian motion. We show how to efficiently estimate the...

In this paper we consider a generalization of one of the earliest models of an asset price, namely the Black–Scholes model, which captures the subdiffusive nature of an asset price dynamics. We introduce the geometric Brownian motion time-changed by infinitely divisible inverse subordinators,...

The main purpose of the paper is to present, how derivatives valuing methodology, known from financial and commodities markets, can be applied to the electricity market. We compare an application of three recent models. We start with the convenience yield approach, then we analyse the...

In this paper we investigate the relationship between spot and futures prices within the EU-wide CO2 emissions trading scheme (EU-ETS). We conduct an empirical study on price behavior, volatility term structure and correlations in different CO2 EU Allowance (EUA) contracts during the pilot...