Modeling electricity spot prices: Regime switching models with price-capped spike distributions

We calibrate Markov regime-switching (MRS) models to spot (log-)prices from two major power markets. We show that while the price-capped (or truncated) spike distributions do not give any advantage over the standard specification in case of moderately spiky markets (such as NEPOOL), they improve the fit and yield significantly different results in case of extremely spiky markets (such as the Australian NSW market).Electricity spot price; Markov regime-switching model; Price spike; Price cap; Truncated distribution

Efficient estimation of Markov regime-switching models: An application to electricity spot prices

In this paper we discuss the calibration of models built on mean-reverting processes combined with Markov regime-switching (MRS). We propose a method that greatly reduces the computational burden induced by the introduction of independent regimes and perform a simulation study to test its efficiency. Our method allows for a 100 to over 1000 times faster calibration than in case of a competing approach utilizing probabilities of the last 10 observations. It is also more general and admits any value of gamma in the base regime dynamics. Since the motivation for this research comes from a recent stream of literature in energy economics, we apply the new method to sample series of electricity spot prices from the German EEX and Australian NSW markets. The proposed MRS models fit these datasets well and replicate the major stylized facts of electricity spot price dynamics.Markov regime-switching; Energy economics; Electricity spot price; EM algorithm; Independent regimes;

An empirical comparison of alternate regime-switching models for electricity spot prices

One of the most profound features of electricity spot prices are the price spikes. Markov regime-switching (MRS) models seem to be a natural candidate for modeling this spiky behavior. However, in the studies published so far, the goodness-of-fit of the proposed models has not been a major focus. While most of the models were elegant, their fit to empirical data has either been not examined thoroughly or the signs of a bad fit ignored. With this paper we want to fill the gap. We calibrate and test a range of MRS models in an attempt to find parsimonious specifications that not only address the main characteristics of electricity prices but are statistically sound as well. We find that the best structure is that of an independent spike 3-regime model with heteroscedastic diffusion-type base regime dynamics and shifted spike regime distributions. Not only does it allow for consecutive spikes or price drops, which is consistent with market observations, but also exhibits the ‘inverse leverage effect’ reported in the literature for spot electricity prices

Goodness-of-fit testing for regime-switching models

In this paper we propose a novel goodness-of-fit testing scheme for regime-switching models. We consider models with an observable, as well as, a latent state process. The test is based on the Kolmogorov-Smirnov supremum-distance statistic and the concept of the weighted empirical distribution function. We apply the proposed scheme to test whether a 2-state Markov regime-switching model fits electricity spot price data.Regime-switching; Goodness-of-fit; Weighted empirical distribution function; Kolmogorov-Smirnov test

Efficient estimation of Markov regime-switching models: An application to electricity wholesale market prices

In this paper we discuss the calibration issues of models built on mean-reverting processes combined with Markov switching. Due to the unobservable switching mechanism, estimation of Markov regime-switching (MRS) models requires inferring not only the model parameters but also the state process values at the same time. The situation becomes more complicated when the individual regimes are independent from each other and at least one of them exhibits temporal dependence (like mean reversion in electricity spot prices). Then the temporal latency of the dynamics in the regimes as to be taken into account. In this paper we propose a method that greatly reduces the computational burden induced by the introduction of independent regimes in MRS models. We perform a simulation study to test the efficiency of the proposed method and apply it to a sample series of wholesale electricity spot prices from the German EEX market. The proposed 3-regime MRS model fits this data well and also contains unique features that allow for useful interpretations of the price dynamics.Markov regime-switching; heteroskedasticity; EM algorithm; independent regimes; electricity spot price

Regime-switching models for electricity spot prices: Introducing heteroskedastic base regime dynamics and shifted spike distributions

We calibrate Markov regime-switching (MRS) models to mean daily spot prices from the EEX market. Our empirical study shows that (i) models with shifted spike regime distributions lead to more realistic models of electricity spot prices and that (ii) introducing heteroskedasticity in the base regime leads to better spike identification and goodness-of-fit than in MRS models with the standard mean-reverting, constant volatility dynamics.regime-switching, heteroskedasticity, electricity spot price

Building Loss Models

This paper is intended as a guide to building insurance risk (loss) models. A typical model for insurance risk, the so-called collective risk model, treats the aggregate loss as having a compound distribution with two main components: one characterizing the arrival of claims and another describing the severity (or size) of loss resulting from the occurrence of a claim. In this paper we first present efficient simulation algorithms for several classes of claim arrival processes. Then we review a collection of loss distributions and present methods that can be used to assess the goodness-of-fit of the claim size distribution. The collective risk model is often used in health insurance and in general insurance, whenever the main risk components are the number of insurance claims and the amount of the claims. It can also be used for modeling other non-insurance product risks, such as credit and operational risk.Insurance risk model; Loss distribution; Claim arrival process; Poisson process; Renewal process; Random variable generation; Goodness-of-fit testing;

Building Loss Models

This paper is intended as a guide to building insurance risk (loss) models. A typical model for insurance risk, the so-called collective risk model, treats the aggregate loss as having a compound distribution with two main components: one characterizing the arrival of claims and another describing the severity (or size) of loss resulting from the occurrence of a claim. In this paper we first present efficient simulation algorithms for several classes of claim arrival processes. Then we review a collection of loss distributions and present methods that can be used to assess the goodness-of-fit of the claim size distribution. The collective risk model is often used in health insurance and in general insurance, whenever the main risk components are the number of insurance claims and the amount of the claims. It can also be used for modeling other non-insurance product risks, such as credit and operational risk.Insurance risk model; Loss distribution; Claim arrival process; Poisson process; Renewal process; Random variable generation; Goodness-of-fit testing

Building Loss Models

This paper is intended as a guide to building insurance risk (loss) models. A typical model for insurance risk, the so-called collective risk model, treats the aggregate loss as having a compound distribution with two main components: one characterizing the arrival of claims and another describing the severity (or size) of loss resulting from the occurrence of a claim. In this paper we first present efficient simulation algorithms for several classes of claim arrival processes. Then we review a collection of loss distributions and present methods that can be used to assess the goodness-of-fit of the claim size distribution. The collective risk model is often used in health insurance and in general insurance, whenever the main risk components are the number of insurance claims and the amount of the claims. It can also be used for modeling other non-insurance product risks, such as credit and operational risk