Seasonal and stochastic effects in commodity forward curves

In this paper we develop a new model for the dynamics of forward curves of commodities exhibiting seasonalities, such as natural gas, electricity or agricultural commodities. In the existing literature on the subject, the first state variable in multi-factor models is the commodity price, which combines seasonal and stochastic features and may be unobservable. We propose to use instead the average forward price, which is devoid of seasonality and conveys a more robust representation of the current forward curve level. The second factor in the model is a quantity analogous to the stochastic convenience yield, which accounts for the random changes in the forward curve shape. The well-known cost-of-carry relationship is significantly improved by introducing a deterministic seasonal premium within the convenience yield. We develop model estimation procedures and apply them to a number of energy markets.     

Modelling electricity prices: a time change approach

To capture mean reversion and sharp seasonal spikes observed in electricity prices, this paper develops a new stochastic model for electricity spot prices by time changing the Jump Cox-Ingersoll-Ross (JCIR) process with a random clock that is a composite of a Gamma subordinator and a deterministic clock with seasonal activity rate. The time-changed JCIR process is a time-inhomogeneous Markov semimartingale which can be either a jump-diffusion or a pure-jump process, and it has a mean-reverting jump component that leads to mean reversion in the prices in addition to the smooth mean-reversion force. Furthermore, the characteristics of the time-changed JCIR process are seasonal, allowing spikes to occur in a seasonal pattern. The Laplace transform of the time-changed JCIR process can be efficiently computed by Gauss–Laguerre quadrature. This allows us to recover its transition density through efficient Laplace inversion and to calibrate our model using maximum likelihood estimation. To price electricity derivatives, we introduce a class of measure changes that transforms one time-changed JCIR process into another time-changed JCIR process. We derive a closed-form formula for the futures price and obtain the Laplace transform of futures option price in terms of the Laplace transform of the time-changed JCIR process, which can then be efficiently inverted to yield the option price. By fitting our model to two major electricity markets in the US, we show that it is able to capture both the trajectorial and the statistical properties of electricity prices. Comparison with a popular jump-diffusion model is also provided.     

Modelling spikes and pricing swing options in electricity markets

Most electricity markets exhibit high volatilities and occasional distinctive price spikes, which result in demand for derivative products which protect the holder against high prices. In this paper we examine a simple spot price model that is the exponential of the sum of an Ornstein–Uhlenbeck and an independent mean-reverting pure jump process. We derive the moment generating function as well as various approximations to the probability density function of the logarithm of the spot price process at maturity T. Hence we are able to calibrate the model to the observed forward curve and present semi-analytic formulae 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 utilized which in turn uses approximations to the conditional density of the spot process.     

可再生能源电价管制政策的文献综述

可再生能源电力产业的价格方面的管制政策的文献比较多.总体来说这些政策主要涉及可再生能源电价管制政策的分类、相关理论、政策效率和政策的实证方面.本文对可再生能源电价管制政策的相关文献进行了总结和分析,同时提出本文的观点.     

Futures volatility forecasting based on big data analytics with incorporating an order imbalance effect

Future markets play vital roles in supporting economic activities in modern society. For example, crude oil and electricity futures markets have heavy effects on a nation’s energy operation management. Thus, volatility forecasting of the futures market is an emerging but increasingly influential field of financial research. In this paper, we adopt big data analytics, called Extreme Gradient Boosting (XGBoost) from computer science, in an attempt to improve the forecasting accuracy of futures volatility and to demonstrate the application of big data analytics in the financial spectrum in terms of volatility forecasting. We further unveil that order imbalance estimation might incorporate abundant information to reflect price jumps and other trading information in the futures market. Including order imbalance information helps our model capture underpinned market rules such as supply and demand, which lightens the information loss during the model formation. Our empirical results suggest that the volatility forecasting accuracy of the XGBoost method considerably beats the GARCH-jump and HAR-jump models in both crude oil futures market and electricity futures market. Our results could also produce plentiful research implications for both policy makers and energy futures market participants.     

A mixed C-vine copula model for hedging price and volumetric risk in wind power trading

When energy trading companies enter into long-term agreements with wind power producers, where a fixed price is paid for the fluctuating production, they are facing a joint price and volumetric risk. Since the pay-off of such agreements is non-linear, a hedging portfolio would ideally consist of not only forwards, but also a basket of e.g. call and put options. Illiquidity and an almost non-existent market for options challenge however the optimal hedging of joint price and volumetric risk in many market places. Here, we consider the case of the Danish power market, and exploit its strong positive correlation with the much more liquid German market to construct a proxy hedge. We propose a three-dimensional mixed vine copula to model the evolution of the Danish and German spot electricity prices and the Danish wind power production. We construct a realistic hedging portfolio by identifying various instruments available in the market, such as real options in the form of the right to transfer electricity across the border and the right to convert electricity to heat. Using the proposed vine copula to determine optimal hedging decisions, we show that significant benefits are to be drawn by extending the hedging portfolio with the proposed instruments.     

A spot market model for pricing derivatives in electricity markets

Abstract

In this paper, we analyse the evolution of prices in deregulated electricity markets. We present a general model that simultaneously takes into account the following features: seasonal patterns, price spikes, mean reversion, price dependent volatilities and long term non-stationarity. We estimate the parameters of the model using historical data from the European Energy Exchange. Finally, we demonstrate how it can be used for pricing derivatives via Monte Carlo simulation.     

On the seasonality in the implied volatility of electricity options

Seasonality is an important topic in electricity markets, as both supply and demand are dependent on the time of the year. Clearly, the level of prices shows a seasonal behaviour, but not only this. Also, the price fluctuations are typically seasonal. In this paper, we study empirically the implied volatility of options on electricity futures, investigate whether seasonality is present and we aim at quantifying its structure. Although typically futures prices can be well described through multi-factor models including exponentially decreasing components, we do not find evidence of exponential behaviour in our data set. Generally, a simple linear shape reflects the squared volatilities very well as a curve depending on the time to maturity. Moreover, we find that the level of volatility exhibits clear seasonal patterns that depend on the delivery month of the futures. Furthermore, in an out-of-sample analysis we compare the performance of several implementations of seasonality in the one-factor framework.     

Spot and derivative pricing in the EEX power market

Using spot and futures price data from the German EEX Power market, we test the adequacy of various one-factor and two-factor models for electricity spot prices. The models are compared along two different dimensions: (1) We assess their ability to explain the major data characteristics and (2) the forecasting accuracy for expected future spot prices is analyzed. We find that the regime-switching models clearly outperform its competitors in almost all respects. The best results are obtained using a two-regime model with a Gaussian distribution in the spike regime. Furthermore, for short and medium-term periods our results underpin the frequently stated hypothesis that electricity futures quotes are consistently greater than the expected future spot, a situation which is denoted as contango.     

Estimating affine multifactor term structure models using closed-form likelihood expansions

We develop and implement a technique for closed-form maximum likelihood estimation (MLE) of multifactor affine yield models. We derive closed-form approximations to likelihoods for nine Dai and Singleton (2000) affine models. Simulations show our technique very accurately approximates true (but infeasible) MLE. Using US Treasury data, we estimate nine affine yield models with different market price of risk specifications. MLE allows non-nested model comparison using likelihood ratio tests; the preferred model depends on the market price of risk. Estimation with simulated and real data suggests our technique is much closer to true MLE than Euler and quasi-maximum likelihood (QML) methods.     

AN EMPIRICAL STUDY OF A NEW CLASS OF NO-ARBITRAGE-BASED DISCRETE MODELS OF THE TERM STRUCTURE

We present empirical tests of the new no-arbitrage-based term structure paradigm in discrete time. We derive and test empirical specifications for deterministic one-factor forward rate volatility models and examine the compatibility of these forward rate volatility functions using term structure dynamics. Our estimation technique uses the generalized method of moments and is based on forward bond price deviations. We do not impose restrictions on the market price of risk, and we incorporate all available term structure information. Our data consist of four sets of pure discount bonds derived from the CRSP bond files and U.S. Treasury bill quotes.     

Modelling the joint behaviour of electricity prices in interconnected markets

The liberalization of energy markets worldwide during recent decades has introduced severe implications for the price formation in these markets. Especially within the European day-ahead electricity markets, increased physical connections between different market areas and a joint effort on optimizing the aggregate social welfare have led to highly connected markets. Consequently, observing the exact same hourly day-ahead prices for two or more interconnected electricity markets in Europe happens frequently. This affects the modelling of such prices and in turn the valuation of derivatives written on prices from these market areas. In this paper, we propose a joint model for day-ahead electricity prices in interconnected markets composed of a combination of transformed Ornstein–Uhlenbeck processes. We discuss the properties of the model and propose an estimation procedure based on filtering techniques. Furthermore, the properties of the model reveal that analytical prices are attainable for, e.g., forwards and spread options.     

Dynamic copula models for the spark spread

We propose a non-symmetric copula to model the evolution of electricity and gas prices by a bivariate non-Gaussian autoregressive process. We identify the marginal dynamics as driven by normal inverse Gaussian processes, estimating them from a series of observed UK electricity and gas spot data. We estimate the copula by modeling the difference between the empirical copula and the independent copula. We then simulate the joint process and price options written on the spark spread. We find that option prices are significantly influenced by the copula and the marginal distributions, along with the seasonality of the underlying prices.     

Fixed price and book building methods in an exogenous environment: Evidence from Indonesia stock market

Book building has become a popular method of selling new shares. Although previous models suggest that book building is an efficient method for price discovery in initial public offering (IPO) issuance, empirical evidence provides mixed results. Previous empirical findings on IPO methods have been obtained from markets that allow issuers to choose the IPO method, and this setting is not free from endogeneity issues. We investigate the effect of IPO method (fixed price vs book building) in Indonesia, which is an emerging market that offers an exogenous setting for IPO methods. More specifically, Indonesia used the fixed price method for IPOs before October 2000 and used the book building method thereafter following the introduction of new IPO regulations. Using estimation methods that consider clustering phenomena, we find that book building yields larger underpricing and greater volatility than the fixed price method. Moreover, a positive relationship is observed between underpricing and aftermarket volatility for the book building method and book building IPOs underperform fixed price IPOs. No relationship was observed between underpricing and long-term performance for book building IPOs. Compared with previous models, our findings suggest that book building does not represent a quality IPO method and suffers from agency conflict; thus, this method needs improvement.     

The Relationship Between Energy Commodity Prices and Electricity and Market Index Performances: Evidence from an Emerging Market

We investigate the effect of energy commodity price movements on market and electricity index returns in Turkey for the periods before, during, and after the year 2008. Although the Turkish economy is highly reliant on oil, we find that oil price does not lead either electricity or market indexes. This might be attributable to sluggish integration of financial markets in Turkey compared to developed markets. Natural gas price leads electricity index in the pre-2008 period. Its significance is reduced following the decline in natural gas usage in electricity production. This suggests that commodity dependence may be driving the link between commodity and asset prices in related sectors.     

The bias in Black-Scholes/Black implied volatility: An analysis of equity and energy markets

In this paper we examine the extent of the bias between Black and Scholes (1973)/Black (1976) implied volatility and realized term volatility in the equity and energy markets. Explicitly modeling a market price of volatility risk, we extend previous work by demonstrating that Black-Scholes is an upward-biased predictor of future realized volatility in S&P 500/S&P 100 stock-market indices. Turning to the Black options-on-futures formula, we apply our methodology to options on energy contracts, a market in which crises are characterized by a positive correlation between price-returns and volatilities: After controlling for both term-structure and seasonality effects, our theoretical and empirical findings suggest a similar upward bias in the volatility implied in energy options contracts. We show the bias in both Black-Scholes/Black implied volatilities to be related to a negative market price of volatility risk. JEL Classification G12 · G13     

Price Indices Based on the Hedonic Repeat-Sales Method: Application to the Housing Market

Shiller (1993) proposes the hedonic repeated-measures (HRM) approach to measuring constant quality price indices for heterogeneous assets such as some bonds and real estate. We derive a mathematical relationship between the coefficients of the HRM model and those from the standard repeat-sales model, and we demonstrate how hedonic characteristics should be chosen for inclusion in the HRM model. Empirical estimates using Fairfax, Virginia, housing transactions data show that the HRM price index evaluated at the mean of the hedonic variable is virtually identical to the standard repeat sales index, just as predicted by our mathematical relationship. But the HRM allows estimation of different price paths for heterogeneous assets. We demonstrate that use of assessed value as the only hedonic characteristic allows parsimonious HRM estimates.     

Location-specific stock market indices: an exploration

This article develops an alternative location-specific stock market index driven by investors’ ‘attachment’ towards investment at a specific location. We evaluate the performance of hypothetical stock market indices that track companies based on their state of registration, taking the US stock market as our case. Using annual data since 1980 we present raw, risk-adjusted and value-weighted state portfolios’ returns to study the extent to which stock market performance varies by state-level demographics and economic factors. A dynamic panel data estimation – with and without spatial spillover effects – is employed to establish a strong association between stock price performance and the state-level (or geography-weighted) factors. We find that spatial effects are strong and that the ‘spatial attachment’ of companies in interaction with the various location-specific variables imparts an overarching influence on stock-price performance. Comparison of model performances further supports our claims.     

Estimation in English auctions with unobserved heterogeneity

We propose a framework for identification and estimation of a private values model with unobserved heterogeneity from bid data in English auctions, using variation in the number of bidders across auctions, and extend the framework to settings where the number of bidders is not cleanly observed in each auction. We illustrate our method on data from eBay Motors auctions. We find that unobserved heterogeneity is important, accounting for two thirds of price variation after controlling for observables, and that welfare measures would be dramatically misestimated if unobserved heterogeneity were ignored.     

Forecasting stock market returns: The sum of the parts is more than the whole

We propose forecasting separately the three components of stock market returns—the dividend–price ratio, earnings growth, and price–earnings ratio growth—the sum-of-the-parts (SOP) method. Our method exploits the different time series persistence of the components and obtains out-of-sample R-squares (compared with the historical mean) of more than 1.3% with monthly data and 13.4% with yearly data. This compares with typically negative R-squares obtained in a similar experiment with predictive regressions. The performance of the SOP method comes mainly from the dividend–price ratio and earnings growth components, and the robustness of the method is due to its low estimation error. An investor who timed the market using our method would have had a Sharpe ratio gain of 0.3.