Rafał Weron

Estimating long range dependence: finite sample properties and confidence intervals

A major issue in financial economics is the behavior of asset returns over long horizons. Various estimators of long range dependence have been proposed. Even though some have known asymptotic properties, it is important to test their accuracy by using simulated series of different lengths. We test R/S analysis, Detrended Fluctuation Analysis and periodogram regression methods on samples drawn from Gaussian white noise. The DFA statistics turns out to be the unanimous winner. Unfortunately, no asymptotic distribution theory has been derived for this statistics so far. We were able, however, to construct empirical (i.e. approximate) confidence intervals for all three methods. The obtained values differ largely from heuristic values proposed by some authors for the R/S statistics and are very close to asymptotic values for the periodogram regression method.

Statistical Tools for Finance and Insurance

Statistical Tools for Finance and Insurance presents ready-to-use solutions, theoretical developments and method construction for many practical problems in quantitative finance and insurance. Written by practitioners and leading academics in the field this book offers a unique combination of topics from which every market analyst and risk manager will benefit. Features of the book: Offers insight into new methods and the applicability of the stochastic technology; Provides the tools, instruments and (online) algorithms for recent techniques in quantitative finance and modern treatments in insurance calculations; Covers topics such as heavy tailed distributions, implied trinomial trees, support vector machines, valuation of mortgage-backed securities, pricing of CAT bonds, simulation of risk processes, and ruin probability approximation; Presents extensive examples; The downloadable electronic edition of the book offers interactive tools.

On the Chambers-Mallows-Stuck method for simulating skewed stable random variables

In the paper Weron (1996, Statist. Probab. Lett. 28, 165-171), I gave a proof to the equality in law of a skewed stable variable and a nonlinear transformation of two independent uniform and exponential variables. The Chambers et al. (1976, J. Amer. Statist. Assoc. 71, 340–344) method of computer generation of a skewed stable random variable is based on this equality. Unfortunately an error crept into my calculations for alpha=1. This note corrects the error.

Hurst analysis of electricity price dynamics

The price of electricity is extremely volatile, because electric power cannot be economically stored, end user demand is largely weather dependent, and the reliability of the grid is paramount. However, underlying the process of price returns is a strong mean-reverting mechanism. We study this feature of electricity returns by means of Hurst R/S analysis.

Modeling electricity loads in California: ARMA models with hyperbolic noise

In this paper we address the issue of modeling and forecasting electricity loads. We apply a two-step procedure to a series of system-wide loads from the California power market. First, we remove the weekly and annual seasonalities. Then, after analyzing properties of the deseasonalized data we fit an autoregressive moving average model. The obtained residuals seem to be independent but with tails heavier than Gaussian. It turns out that the hyperbolic distribution provides an excellent fit. As a justification for our approach we supply out-of-sample forecasts. As it turns out, our method performs significantly better than the one used by the California System Operator.

Modeling highly volatile and seasonal markets: evidence from the Nord Pool electricity market

In this paper we address the issue of modeling spot electricity prices. After analyzing factors leading to the unobservable in other financial or commodity markets price dynamics we propose a mean reverting jump diffusion model. We fit the model to data from the Nord Pool power exchange and find that it nearly duplicates the spot price’s main characteristics. The model can thus be used for risk management and pricing derivatives written on the spot electricity price.

Energy price risk management

The price of electricity is far more volatile than that of other commodities normally noted for extreme volatility. Demand and supply are balanced on a knife-edge because electric power cannot be economically stored, end user demand is largely weather dependent, and the reliability of the grid is paramount. The possibility of extreme price movements increases the risk of trading in electricity markets. However, a number of standard financial tools cannot be readily applied to pricing and hedging electricity derivatives. In this paper we present arguments why this is the case.

Convenience Yields for CO2 Emission Allowance Futures Contracts

In January 2005 the EU-wide CO2 emissions trading system (EU-ETS) has formally entered into operation. Within the new trading system, the right to emit a particular amount of CO2 becomes a tradable commodity - called EU Allowances (EUAs) - and affected companies, traders and investors will face new strategic challenges. In this paper we investigate the nature of convenience yields for CO2 emission allowance futures. We conduct an empirical study on price behavior, volatility term structure and correlations in different CO2 EUA contracts. Our findings are that the market has changed from initial backwardation to contango with significant convenience yields in future contracts for the Kyoto commitment period starting in 2008. A high fraction of the yields can be explained by the price level and volatility of the spot prices. We conclude that the yields can be interpreted as market expectation on the price risk of CO2 emissions allowance prices and the uncertainty of EU allocation plans for the Kyoto period.

A simple model of price formation

A simple Ising spin model, which can describe the mechanism of price formation in financial markets is proposed. In contrast to other agent-based models, the influence does not flow inward from the surrounding neighbors to the center site, but spreads outward from the center to the neighbors. The model thus describes the spread of opinions among traders. It is shown via standard Monte Carlo simulations that very simple rules lead to dynamics that duplicate those of asset prices.

An empirical comparison of alternative schemes for combining electricity spot price forecasts

In this paper we investigate the use of forecast averaging for electricity spot prices. While there is an increasing body of literature on the use of forecast combinations, there is only a small number of applications of these techniques in the area of electricity markets. In this comprehensive empirical study we apply seven averaging and one selection scheme and perform a backtesting analysis on day-ahead electricity prices in three major European and US markets. Our findings support the additional benefit of combining forecasts for deriving more accurate predictions, however, the performance is not uniform across the considered markets. Interestingly, equally weighted pooling of forecasts emerges as a viable robust alternative compared with other schemes that rely on estimated combination weights. Overall, we provide empirical evidence that also for the extremely volatile electricity markets, it is beneficial to combine forecasts from various models for the prediction of day-ahead electricity prices. In addition, we empirically demonstrate that not all forecast combination schemes are recommended.