The forward premium in electricity futures

Understanding the nature of the forward premium is particularly crucial, but rather elusive, for a non-storable commodity such as wholesale electricity. Whilst forward prices emerge as the expectation of spot plus, or minus, an ex ante premium for risk, the manifestation and empirical analysis must focus upon realised ex post premiums. This presents modelling requirements to control for shocks to the spot expectation as well as the endogeneity of ex post premia with spot price outcomes. In addition, because electricity is a derived commodity in the sense that market prices are often set by technologies that convert gas or coal into power, it is an open question whether much of the premia in power may actually be a pass-through of the premia in gas (or coal). Using a four dimensional VAR model we are able to distinguish fundamental and behavioural aspects of price formation in both the daily and monthly forward premia from the British market. We present new evidence on daily and seasonal sign reversals, associated with demand cycles, the greater importance of behavioural adaptations in the risk premia than fundamental or spot market risk measures, and the substantial fuel risk pass-through. We also show the value of a nonlinear specification in this context.     

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.     

Macroeconomic Conditions and the Puzzles of Credit Spreads and Capital Structure

I build a dynamic capital structure model that demonstrates how business cycle variation in expected growth rates, economic uncertainty, and risk premia influences firms' financing policies. Countercyclical fluctuations in risk prices, default probabilities, and default losses arise endogenously through firms' responses to macroeconomic conditions. These comovements generate large credit risk premia for investment grade firms, which helps address the credit spread puzzle and the under‐leverage puzzle in a unified framework. The model generates interesting dynamics for financing and defaults, including market timing in debt issuance and credit contagion. It also provides a novel procedure to estimate state‐dependent default losses.     

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.     

An Anatomy of Commodity Futures Risk Premia

We identify two types of risk premia in commodity futures returns: spot premia related to the risk in the underlying commodity, and term premia related to changes in the basis. Sorting on forecasting variables such as the futures basis, return momentum, volatility, inflation, hedging pressure, and liquidity results in sizable spot premia between 5% and 14% per annum and term premia between 1% and 3% per annum. We show that a single factor, the high‐minus‐low portfolio from basis sorts, explains the cross‐section of spot premia. Two additional basis factors are needed to explain the term premia.     

Rational Expectations and Risk Premia in Forward Markets: Primary Metals at the London Metals Exchange

This paper tests whether forward prices equal the traders' expectations of the future spot prices at maturity, under two different models of expectations formation: full information rational expectations and incomplete information mechanical forecasting rule. The tests are performed, over the period January 1970 through September 1980, on the forward markets for the primary metals—copper, tin, lead, and zinc-traded in the London Metals Exchange. We find evidence consistent with the existence of time varying risk premia.     

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.     

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.     

Joint econometric modeling of spot electricity prices, forwards and options

We propose a joint modeling of spot electricity prices, forwards prices and other derivative prices, using recent developments in discrete time asset pricing methods based on the notions of stochastic discount factor and of Compound Autoregressive (or affine) stochastic processes. We show that this approach provides quasi explicit formulae for forward and option prices, while allowing for a large flexibility in the modeling of dynamics, spikes and seasonality, both in the historical and the risk neutral worlds. We also propose a variety of inference techniques involving inversion methods, the Kalman filter and the Kitagawa?CHamilton filter. Finally, an application based on French spot prices and forward products is proposed.     

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.     

Modelling jumps in electricity prices: theory and empirical evidence

Objective of this paper is to enhance the understanding of modelling jumps and to analyse the model risk based on the jump component in electricity markets. We provide a common modelling framework that allows to incorporate the main jump patterns observed in electricity spot prices and compare the effectiveness of different jump specifications. To this end, we calibrate the models to daily European Energy Exchange (EEX) market data through Markov Chain Monte Carlo based methods. To assess the quality of the estimated jump processes, we analyse their trajectorial and statistical properties. Moreover, even when the models are calibrated to a cross-section of derivative prices substantial model risk remains.      

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.     

Consumption, Dividends, and the Cross Section of Equity Returns

We show that aggregate consumption risks embodied in cash flows can account for the puzzling differences in risk premia across book‐to‐market, momentum, and size‐sorted portfolios. The dynamics of aggregate consumption and cash flow growth rates, modeled as a vector autoregression, are used to measure the consumption beta of discounted cash flows. Differences in these cash flow betas account for more than 60% of the cross‐sectional variation in risk premia. The market price for risk in cash flows is highly significant. We argue that cash flow risk is important for interpreting differences in risk compensation across assets.     

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.     

Electricity Prices and Power Derivatives: Evidence from the Nordic Power Exchange

This paper examines the importance of the regular pattern in the behavior of electricity prices, and its implications for the purposes of derivative pricing. We analyze the Nordic Power Exchange's spot, futures, and forward prices. We conclude that the seasonal systematic pattern throughout the year, in particular, is of crucial importance in explaining the shape of the futures/forward curve. Moreover, in the context of the oneand two factor models analyzed in this paper, a simple sinusoidal functionis adequate in order capture the seasonal pattern of the features and forwardcurve directly implied by the seasonal behavior of spot electricity prices.     

Innovation,Growth, and Asset Prices

We examine the asset pricing implications of a production economy whose long‐term growth prospects are endogenously determined by innovation and R&D. In equilibrium, R&D endogenously drives a small, persistent component in productivity that generates long‐run uncertainty about economic growth. With recursive preferences, households fear that persistent downturns in economic growth are accompanied by low asset valuations and command high‐risk premia in asset markets. Empirically, we find substantial evidence for innovation‐driven low‐frequency movements in aggregate growth rates and asset market valuations. In short, equilibrium growth is risky.     

The value of risk in real estate markets

In this article we test the urban asset pricing model of Capozza and Sick (1988) and focus on the empirical dimensions of the effects of risk on urban land prices. The effects of systematic and unsystematic risk are distinguished in the model which incorporates the value of the option to convert land to urban uses into the pricing of urban real estate. We find the value of systematic risk in our Canadian urban areas to be negative and highly statistically significant. We find that approximately 2.5 percent of the value of houses in our sample arises from systematic risk. In our sample, unsystematic risk is a larger proportion of total risk than systematic risk. Therefore, most of the effect of total risk may be ascribed to unsystematic risk. The effect of total risk on land prices is illustrated through the irreversibility premia estimates. These premia vary greatly in size and statistical significance. Thus, the effect of unsystematic risk is highly city specific. In the two regions where the irreversibility premia are statistically significant, it accounts for 22 percent and 53 percent of the average housing price; thus, unsystematic risk can be a very important determinant of housing prices.These results highlight the importance of risk in determining urban land prices. The value of the option to convert land to urban uses imparts considerable value to developed land and must be considered when evaluating interurban area price differences.     

A Search-Based Theory of the On-the-Run Phenomenon

We propose a model in which assets with identical cash flows can trade at different prices. Infinitely lived agents can establish long positions in a search spot market, or short positions by first borrowing an asset in a search repo market. We show that short-sellers can endogenously concentrate in one asset because of search externalities and the constraint that they must deliver the asset they borrowed. That asset enjoys greater liquidity, a higher lending fee ("specialness"), and trades at a premium consistent with no-arbitrage. We derive closed-form solutions for small frictions, and provide a calibration generating realistic on-the-run premia.     

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.