Electricity Forward Prices: A High-Frequency Empirical Analysis

We conduct an empirical analysis of forward prices in the PJM electricity market using a high‐frequency data set of hourly spot and day‐ahead forward prices. We find that there are significant risk premia in electricity forward prices. These premia vary systematically throughout the day and are directly related to economic risk factors, such as the volatility of unexpected changes in demand, spot prices, and total revenues. These results support the hypothesis that electricity forward prices in the Pennsylvania, New Jersey, and Maryland market are determined rationally by risk‐averse economic agents.     

Equilibrium Pricing and Optimal Hedging in Electricity Forward Markets

Spot power prices are volatile and since electricity cannot be economically stored, familiar arbitrage-based methods are not applicable for pricing power derivative contracts. This paper presents an equilibrium model implying that the forward power price is a downward biased predictor of the future spot price if expected power demand is low and demand risk is moderate. However, the equilibrium forward premium increases when either expected demand or demand variance is high, because of positive skewness in the spot power price distribution. Preliminary empirical evidence indicates that the premium in forward power prices is greatest during the summer months.     

THE POSSIBILITY OF ESTIMATING RISK PREMIA IN ASSET PRICING MODELS

The authors show that estimates of risk premia on the market based on capital asset pricing models or arbitrage pricing theories can only be estimates of the ex post or sample risk premium on the market and cannot be interpreted as better estimates of the ex ante premium than those provided by sample averages of data. The ex ante premium drops out of the generating function for the returns used in the second-pass regressions. Although previous estimates of nonmarket premia have failed to take appropriate account of the population mean, that mean can in fact be estimated and appropriate adjustments made. Various approaches to estimating the ex ante risk premium and the population mean are discussed.     

Stochastic Convenience Yield Implied from Commodity Futures and Interest Rates

We characterize a three‐factor model of commodity spot prices, convenience yields, and interest rates, which nests many existing specifications. The model allows convenience yields to depend on spot prices and interest rates. It also allows for time‐varying risk premia. Both may induce mean reversion in spot prices, albeit with very different economic implications. Empirical results show strong evidence for spot‐price level dependence in convenience yields for crude oil and copper, which implies mean reversion in prices under the risk‐neutral measure. Silver, gold, and copper exhibit time variation in risk premia that implies mean reversion of prices under the physical measure.     

Implied Foreign Exchange Risk Premia

This paper uses implied volatilities from foreign exchange option prices and the results of no‐arbitrage theory to estimate foreign exchange risk premia. In particular, under the assumption of no‐arbitrage, the foreign exchange risk premium is driven by the difference between investors’ market prices of risk in the two currencies. In an international economy with three currencies, sterling, US dollar and Deutschemark, we can use the information on implied volatilities of the three cross rates to derive estimates of implied or ex ante market prices of risk and of foreign exchange risk premia. The foreign exchange risk premia estimates are then compared to survey‐based risk premia.     

Limits to arbitrage and hedging: Evidence from commodity markets

We build an equilibrium model of commodity markets in which speculators are capital constrained, and commodity producers have hedging demands for commodity futures. Increases in producers' hedging demand or speculators' capital constraints increase hedging costs via price-pressure on futures. These in turn affect producers' equilibrium hedging and supply decision inducing a link between a financial friction in the futures market and the commodity spot prices. Consistent with the model, measures of producers' propensity to hedge forecasts futures returns and spot prices in oil and gas market data from 1979 to 2010. The component of the commodity futures risk premium associated with producer hedging demand rises when speculative activity reduces. We conclude that limits to financial arbitrage generate limits to hedging by producers, and affect equilibrium commodity supply and prices.     

Spot price modeling and the valuation of electricity forward contracts: The role of demand and capacity

We propose a model where wholesale electricity prices are explained by two state variables: demand and capacity. We derive analytical expressions to price forward contracts and to calculate the forward premium. We apply our model to the PJM, England and Wales, and Nord Pool markets. Our empirical findings indicate that volatility of demand is seasonal and that the market price of demand risk is also seasonal and positive, both of which exert an upward (seasonal) pressure on the price of forward contracts. We assume that both volatility of capacity and the market price of capacity risk are constant and find that, depending on the market and period under study, it could either exert an upward or downward pressure on forward prices. In all markets we find that the forward premium exhibits a seasonal pattern. During the months of high volatility of demand, forward contracts trade at a premium. During months of low volatility of demand, forwards can either trade at a relatively small premium or, even in some cases, at a discount, i.e. they exhibit a negative forward premium.     

The Forward Premium in the Nord Pool Power Market

This article investigates the forward premium of futures contracts in the Nordic power market for the time period from January 2004 to December 2013. We find that futures prices are biased predictors of the subsequent spot prices and that there is a significant forward premium in the Nord Pool market, particularly during the winter and autumn. We analyze the impact from several factors on the forward premium. The spot price, and the deviation of water inflow from its usual level, positively affect the forward premium. The variance of the spot price also has a positive effect on the forward premium, but only for the contract closest to delivery.     

The price of power: The valuation of power and weather derivatives

Pricing contingent claims on power presents numerous challenges due to (1) the unique behavior of power prices, and (2) time-dependent variations in prices. We propose and implement a model in which the spot price of power is a function of two state variables: demand (load) and fuel price. In this model, any power derivative price must satisfy a PDE with boundary conditions that reflect capacity limits and the non-linear relation between load and the spot price of power. Moreover, since power is non-storable and demand is not a traded asset, the power derivative price embeds a market price of risk. Using inverse problem techniques and power forward prices from the PJM market, we solve for this market price of risk function. During 1999–2001, the upward bias in the forward price was as large as $50/MWh for some days in July. By 2005, the largest estimated upward bias had fallen to $19/MWh. These large biases are plausibly due to the extreme right skewness of power prices; this induces left skewness in the payoff to short forward positions, and a large risk premium is required to induce traders to sell power forwards. This risk premium suggests that the power market is not fully integrated with the broader financial markets.     

Pricing forward contracts in power markets by the certainty equivalence principle: Explaining the sign of the market risk premium

In this paper we provide a framework that explains how the market risk premium, defined as the difference between forward prices and spot forecasts, depends on the risk preferences of market players and the interaction between buyers and sellers. In commodities markets this premium is an important indicator of the behavior of buyers and sellers and their views on the market spanning between short-term and long-term horizons. We show that under certain assumptions it is possible to derive explicit solutions that link levels of risk aversion and market power with market prices of risk and the market risk premium. We apply our model to the German electricity market and show that the market risk premium exhibits a term structure which can be explained by the combination of two factors. Firstly, the levels of risk aversion of buyers and sellers, and secondly, how the market power of producers, relative to that of buyers, affects forward prices with different delivery periods.     

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.     

Term premium dynamics in an emerging market: Risk,liquidity, and behavioral factors

This paper contributes to the fixed income research by identifying determinants of term premium in an emerging market’s treasury bond yields with particular attention on ambiguity. We use Nelson–Siegel yield curves generated from daily bond price quotes as input to construct a three-factor affine term structure model which decomposes observed yields into risk-neutral and term premium components. We also construct an ambiguity index using intraday FX return data following Brenner and Izhakian (2018). Our analyses suggest that a combination of factors representing market risk, credit risk, liquidity, ambiguity, and investor sentiments can explain majority of the variation in term premia. Explanatory power of credit risk measures are found to increase while those of volatility, ambiguity, and sentiment measures diminish with the maturity horizon. The results imply that ambiguity aversion of bond investors is a major determinant of the shape of the yield curve as it drives the premia for short end of the yield curve lower in line with the expectation of flight-to-safety behavior.     

Optimal Portfolio Choices, House Risk Hedging and the Pricing of Forward House Transactions

This paper develops a utility indifference model for evaluating various prices associated with forward transactions in the housing market, based on the equivalent principle of expected wealth utility derived from the forward and spot real estate markets. Our model results show that forward transactions in the housing market are probably not due to house sellers?? and buyers?? heterogeneity, but to their demand for hedging against house price risk. When the imperfections of real estate markets and the risk preferences of market participants are taken into consideration, we are able to show that the idiosyncratic risk premium, which mainly depends on the participants?? risk preferences and the correlation between the traded asset and the real estate, is a remarkable determinant of house sellers?? and buyers?? forward reservation prices. In addition, we also find that the market clearing forward price usually will not converge toward the expected risk-neutral forward price. The sellers?? or buyers?? risk aversion degrees and market powers are also identified to play crucial roles in determining the clearing forward price.     

Are Housing Price Cycles Driven by Irrational Expectations?

This paper investigates the extent to which condominium apartment prices are set in an efficient asset market. Unlike previous work that focuses on the time-series properties of measures of excess returns, the analysis is framed in terms of the changes in observable house prices over time. More precisely, the paper develops and applies a test of the joint null hypothesis of rational expectations, perfect markets, and no risk premium in the Vancouver condominium apartment market. The empirical results provide significant evidence against the joint null hypothesis. On average, ex post house price changes move in a direction opposite to their rational expectation. This approach offers a methodological advantage over the standard efficiency literature and is shown to provide a more powerful test of market efficiency than conventional return regressions. Another contribution of the paper is to characterize the time-series properties of deviations of condominium prices from those predicted by the risk-neutral rational expectations model, using cointegration and random coefficients techniques. Deviations in house price changes from their (risk-neutral) rational expectations are time varying, stationary, and related to the stage of the real estate price cycle.     

Risk Premia in Foreign Currency Futures

This paper tests the uncorrelatedness of increments of daily foreign currency futures prices and derives implications for risk premia based on a heteroscedasticity-robust variance ratio test. There is evidence suggesting the existence of a time-varying risk premia. Moreover, the results suggest that currency futures price is not an unbiased predictor of currency spot price on corresponding maturity date of currency futures contract. The paper also applies a heteroscedasticity-adjusted Box-Pierce Q test to the same data set for comparison.     

An explanation of the forward premium 'puzzle'

Existing literature reports a puzzle about the forward rate premium over the spot foreign exchange rate. The premium is often negatively correlated with subsequent changes in the spot rate. This defies economic intuition and possibly violates market efficiency. Rational explanations include non-stationary risk premia and econometric mis-specifications, but some embrace the puzzle as a guide to profitable trading.
We suggest there is really no puzzle. A simple model fits the data: forward exchange rates are unbiased predictors of subsequent spot rates. The puzzle arises because the forward rate, the spot rate, and the forward premium follow nearly non-stationary time series processes. We document these properties with an extended sample and show why they give the delusion of a puzzle.     

Estimating Early Exercise Premiums on Gold and Copper Options Using a Multifactor Model and Density Matched Lattices

We use the standard geometric Brownian motion augmented by jumps to describe the spot underlying and mean regressive models of interest rates and convenience yields as state variables for gold and copper prices. Estimates of parameters of the diffusion processes are obtained by the Kalman filter. Using these estimates, jump parameters are estimated in the second stage by least squares. Early exercise premia on puts and calls are computed using a lattice with probabilities assigned by the density matching technique. We find that while deep in the money options have greater absolute early exercise premiums, the early exercise premium is roughly constant as a percent of option price. Our findings also confirm that gold behaves like an investment asset and copper behaves like a commodity.     

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.     

THE DIFFERENTIAL EFFECTS OF SINKING FUNDS ON BOND RISK PREMIA

This study analyzes the effect that two options created by the inclusion of a sinking fund clause in a bond indenture have on the bond issue's secondary market risk premium. The impact of market prices that exceed current sinking fund redemption prices, and of par versus premium redemption, is clearly apparent when a set of issue-specific and macroeconomic control variables are incorporated into a model of bond risk premia. Thus, secondary market prices for the large-volume utility bond transactions in the sample reflect knowledge of individual-issue, time-varying indenture characteristics.     

Forward exchange rates in general equilibrium

This paper develops a two-country, overlapping-generations model of an economy with a forward market in foreign exchange. The equilibrium forward rate exhibits the conventional decomposition into the expected future spot rate, a convexity term and a risk premium. Unlike partial equilibrium models, however, the model expresses these terms as functions of the primitive structural parameters of the economy. It thus provides insights into the structure of the premium which may facilitate interpretation of empirical studies of the forward markets. In particular, it suggests that time-varying risk premia may arise from changes in the distribution of wealth between countries over time.