Pricing swing options and other electricity derivatives

The deregulation of regional electricity markets has led to more competitive prices but also higher uncertainty in the future electricity price development. Most markets exhibit high volatilities and occasional distinctive price spikes, which results in demand for derivative products which protect the holder against high prices. A good understanding of the stochastic price dynamics is required for the purposes of risk management and pricing derivatives. In this thesis we examine a simple spot price model which is the exponential of the sum of an Ornstein-Uhlenbeck and an independent pure jump process. We derive the moment generating function as well as various approximations to the probability density function of the logarithm of this spot price process at maturity T. With some restrictions on the set of possible martingale measures we show that the risk neutral dynamics remains within the class of considered models and hence we are able to calibrate the model to the observed forward curve and present semi-analytic formulas for premia of path-independent options as well as approximations to call and put options on forward contracts with and without a delivery period. In order to price path-dependent options with multiple exercise rights like swing contracts a grid method is utilised which in turn uses approximations to the conditional density of the spot process. Further contributions of this thesis include a short discussion of interpolation methods to generate a continuous forward curve based on the forward contracts with delivery periods observed in the market, and an investigation into optimal martingale measures in incomplete markets. In particular we present known results of q-optimal martingale measures in the setting of a stochastic volatility model and give a first indication of how to determine the q-optimal measure for q=0 in an exponential Ornstein-Uhlenbeck model consistent with a given forward curve

Modeling electricity prices: international evidence

This paper analyses the evolution of electricity prices in deregulated markets. We present a general model that simultaneously takes into account the possibility of several factors: seasonality, mean reversion, GARCH behaviour and time-dependent jumps. The model is applied to equilibrium spot prices of electricity markets from Argentina, Australia (Victoria), New Zealand (Hayward), NordPool (Scandinavia), Spain and U.S. (PJM) using daily data. Six different nested models were estimated to compare the relative importance of each factor and their interactions. We obtained that electricity prices are mean-reverting with strong volatility (GARCH) and jumps of time-dependent intensity even after adjusting for seasonality. We also provide a detailed unit root analysis of electricity prices against mean reversion, in the presence of jumps and GARCH errors, and propose a new powerful procedure based on bootstrap techniques

Systematic Features of High-Frequency Volatility in Australian Electricity Markets: Intraday Patterns, Information Arrival and Calendar Effects

This paper investigates the intraday price volatility process in four Australian wholesale electricity markets; namely New South Wales, Queensland, South Australia and Victoria. The data set consists of half-hourly electricity prices and demand volumes over the period 1 January 2002 to 1 June 2003. A range of processes including GARCH, Risk Metrics, normal Asymmetric Power ARCH or APARCH, Student APARCH and skewed Student APARCH are used to model the timevarying variance in prices and the inclusion of news arrival as proxied by the contemporaneous volume of demand, time-of-day, day-of-week and month-of-year effects as exogenous explanatory variables. The skewed Student APARCH model, which takes account of right skewed and fat tailed characteristics, produces the best results in three of the markets with the Student APARCH model performing better in the fourth. The results indicate significant innovation spillovers (ARCH effects)and volatility spillovers (GARCH effects) in the conditional standard deviation equation, even with market and calendar effects included. Intraday prices also exhibit significant asymmetric responses of volatility to the flow of information

Volatility-price relationships in power exchanges: A demand-supply analysis

The evidence of volatility-price dependence observed in previous works (Karakatsani and Bunn 2004; Bottazzi, Sapio and Secchi 2005; Simonsen 2005) suggests that there is more to volatility than simply spikes. Volatility is found to be positively correlated with the lagged price level in settings where market power is likely to be particularly strong (UK on-peak sessions, the CalPX). Negative correlation is instead observed in markets considered to be fairly competitive, such as the NordPool. Prompted by these observations, this paper aims to understand whether volatility-price patterns can be mapped into different degrees of market competition, as the evidence seems to suggest. Price fluctuations are modelled as outcomes of dynamics in both sides of the market - demand and supply, which in turn respond to shocks to the underlying preference and technology fundamentals. Negative volatility-price dependence arises if the market dynamics is accounted for by common shocks which affect valuations uniformly. Positive dependence is related to the impact of asymmetric shocks. The paper shows that under certain conditions, these volatility-price patterns can be used to identify the exercise of market power. Identification is however ruled out if all shocks affect valuations uniformly.Electricity, Market, Volatility, Supply Curve, Demand Curve, Fundamentals, Shocks

Shipping markets and freight rates: an analysis of the Baltic Dry Index

Shipping, although a crucial component of the transportation of commodities worldwide, is hardly present in the finance literature at this point. The first and foremost goal of this paper is to describe and explain from an economic perspective the key features of shipping markets; the second one is to analyze the behavior of freight rates, which define the final cost of an imported commodity. We focus on the major index, the BDI (Baltic Dry Index) and propose some diffusion models able to capture the unique features of its trajectories, namely large swings and continuity. Their performance is exhibited on a database covering the period 1988-2010. Such spot models should facilitate the growth of the market of freight rates options, a safe hedging instrument for farmers and cooperatives that ship their grains to distant destinations

Understanding the fine structure of electricity prices

This paper analyzes the special features of electricity spot prices derived from the physics of this commodity and from the economics of supply and demand in a market pool. Besides mean reversion, a property they share with other commodities, power prices exhibit the unique feature of spikes in trajectories. We introduce a class of discontinuous processes exhibiting a "jump-reversion" component to properly represent these sharp upward moves shortly followed by drops of similar magnitude. Our approach allows to capture—for the first time to our knowledge—both the trajectorial and the statistical properties of electricity pool prices. The quality of the fitting is illustrated on a database of major U.S. power markets

Transmission of prices and price volatility in Australian electricity spot markets: A multivariate GARCH analysis

This paper examines the transmission of spot electricity prices and price volatility among the five Australian electricity markets in the National Electricity Market (NEM): namely, New South Wales (NSW), Queensland (QLD), South Australia (SA), the Snowy Mountains Hydroelectric Scheme (SNO) and Victoria (VIC). A multivariate generalised autoregressive conditional heteroskedasticity (MGARCH) model is used to identify the source and magnitude of spillovers. The results indicate the presence of positive own mean spillovers in only a small number of markets and no mean spillovers between any of the markets. This appears to be directly related to the limitations of the present system of regional interconnectors. Nevertheless, the large number of significant ownvolatility and cross-volatility spillovers in all five markets indicates the presence of strong ARCH and GARCH effects. Contrary to evidence from studies in North American electricity markets, the results also indicate that Australian electricity spot prices are stationary.spot electricity price markets; mean and volatility spillovers; multivariate GARCH