How effective is advertising in duopoly markets?

A simple Ising spin model which can describe the mechanism of advertising in a duopoly market 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 customers. It is shown via standard Monte Carlo simulations that very simple rules and inclusion of an external field - an advertising campaign - lead to phase transitions, ie. extreme and fast changes in market share.advertising, oligopoly, duopoly, Ising model, agent-based model

Heavy-tails and regime-switching in electricity prices

In this paper we first analyze the stylized facts of electricity prices, in particular, the extreme volatility and price spikes which lead to heavy-tailed distributions of price changes. Then we calibrate Markov regime-switching (MRS) models with heavy-tailed components and show that they adequately address the aforementioned characteristics. Contrary to the common belief that electricity price models ‘should be built on log-prices’, we find evidence that modeling the prices themselves is more beneficial and methodologically sound, at least in case of MRS models.Electricity spot price, Heavy-tails, Spikes, Markov regime-switching, Pareto distribution

Heavy tails and electricity prices

In the first years after the emergence of deregulated power markets it became apparent that for the valuation of electricity derivatives we cannot simply rely on models developed for financial or other commodity markets. However, before adequate models can be put forward the unique characteristics of electricity (spot) prices have to be thoroughly analyzed. In particular, the extreme volatility and price spikes which lead to heavy-tailed distributions of returns. In this paper we first analyze the stylized facts of electricity prices, then present two modeling approaches: jump-diffusion and regime-switching, which to some extent address the pertinent issues.Heavy-tailed distribution; Electricity spot price; Seasonality; Volatility; Price spike;

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.Econophysics; Electricity price; Risk management; Mean-reversion;

Levy-stable distributions revisited: tail index > 2 does not exclude the Levy-stable regime

Power-law tail behavior and the summation scheme of Levy-stable distributions is the basis for their frequent use as models when fat tails above a Gaussian distribution are observed. However, recent studies suggest that financial asset returns exhibit tail exponents well above the Levy-stable regime (0Levy-stable distribution; Alpha-stable distribution; Tail exponent; Hill estimator;

Levy-stable distributions revisited: tail index > 2 does not exclude the Levy-stable regime

Power-law tail behavior and the summation scheme of Levy-stable (alpha- stable) distributions is the basis for their frequent use as models when fat tails above a Gaussian distribution are observed. However, recent studies suggest that financial asset returns exhibit tail exponents well above the Levy-stable regime (0Levy-stable distribution, Alpha-stable distribution, Tail exponent, Hill estimator

Forecasting wholesale electricity prices: A review of time series models

In this paper we assess the short-term forecasting power of different time series models in the electricity spot market. We calibrate autoregression (AR) models, including specifications with a fundamental (exogenous) variable - system load, to California Power Exchange (CalPX) system spot prices. Then we evaluate their point and interval forecasting performance in relatively calm and extremely volatile periods preceding the market crash in winter 2000/2001. In particular, we test which innovations distributions/processes - Gaussian, GARCH, heavy-tailed (NIG, alpha-stable) or non-parametric - lead to best predictions.Electricity price forecasting; heavy tailed distribution; autoregression model; GARCH model; non-parametric noise; system load

Performance of the estimators of stable law parameters

In this paper, we discuss the issue of estimation of the parameters of stable laws. We present an overview of the known methods and compare them on samples of different sizes and for different values of the parameters. Performance tables are provided.Stable distribution, Simulation, Random variable

Evolution in a changing environment

We propose a simple model, based on Monte Carlo simulations, for studying the effects of changes in the environment on the adaptation and extinction of evolving species. We show that the geological data of climatic changes are well described by Levy-stable distributions. This leads, in our model, to a fairly good reproduction of the known data on species extinctions. We have also found that the dependence of the probability that a given number of species becomes extinct in one time step, on the number of extinct species shows a cross-over from an exponential to a power-like character.Levy-stable distribution; Monte Carlo simulation; Species extinction; Evolution;

Market price of risk implied by Asian-style electricity options

In this paper we propose a jump diffusion type model which recovers the main characteristics of electricity spot price dynamics, including seasonality, mean reversion, and spiky behavior. Calibration of the market price of risk allows for pricing of Asian-type options written on the spot electricity price traded at Nord Pool. The usefulness of the approach is confirmed by out-of-sample tests.Power market, Electricity price modeling, Asian option, Market price of risk, Derivatives pricing