Spot contract

About: Spot contract is a research topic. Over the lifetime, 3437 publications have been published within this topic receiving 91599 citations.

Phenomenology of the interest rate curve

Abstract: This paper contains a statistical description of the whole U.S. forward rate curve (FRC), based on data from the period 1990-1996. We find that the average deviation of the FRC from the spot rate grows as the square-root of the maturity, with a prefactor which is comparable to the spot rate volatility. This suggests that forward rate market prices include a risk premium, comparable to the probable changes of the spot rate between now and maturity, which can be understood as a ‘Value-at-Risk’ type of pricing. The instantaneous FRC however departs form a simple square-root law. The distortion is maximum around one year, and reflects the market anticipation of a local trend on the spot rate. This anticipated trend is shown to be calibrated on the past behaviour of the spot itself. We show that this is consistent with the volatility ‘hump’ around one year found by several authors (and which we confirm). Finally, the number of independent components needed to interpret most of the FRC fluctuations is found to be small. We rationalize this by showing that the dynamical evolution of the FRC contains a stabilizing second derivative (line tension) term, which tends to suppress short scale distortions of the FRC, suggesting an analogy with the motion of a vibrating string. This shape dependent term could lead, in principle, to arbitrage. However, this arbitrage cannot be implemented in practice because of transaction costs. We suggest that the presence of transaction costs (or other market ‘imperfections’) is crucial for model building, for a much wider class of models becomes eligible to represent reality. Electronic addresses : bouchaud@amoco.saclay.cea.fr cont@ens.fr elkaroui@cmapx.polytechnique.fr nsagna@csfp.co.uk potters@cfm.fr

Electricity price forecasting — ARIMA model approach

Abstract: Electricity price forecasting is becoming more important in everyday business of power utilities. Good forecasting models can increase effectiveness of producers and buyers playing roles in electricity market. Price is also a very important element in investment planning process. This paper presents a forecasting technique to model day-ahead spot price using well known ARIMA model to analyze and forecast time series. The model is applied to time series consisting of day-ahead electricity prices from EPEX power exchange.

12 Modeling Electricity Forward Curve Dynamics in the Nordic Market

Abstract: This chapter considers the modeling of electricity forward curve dynamics with parameterized volatility and correlation structures. We estimate the model parameters by using the Nordic market’s price data and show how the model can be implemented into everyday industry practice. Electricity markets are different from the usual financial markets and many other commodity markets due to the non-storability of electricity. The spot price of electricity is set by the shortterm supply‐demand equilibrium, and supply and demand must be in balance at each instance. Because the demand (supply) today does not necessarily have anything to do with the demand (supply) in the future, the spot electricity today is a different asset from the spot electricity in the future. This implies that the relation between the spot price and the forward prices in the electricity markets is not as straightforward as in the usual financial and commodity markets. In this chapter we develop a simple parameterized model for forward curve dynamics. We estimate the model parameters by using the data from the Nordic electricity market. The Nordic electricity market is hydro-dominated with roughly 50% of the electricity supply being hydrobased. The winters are cold and much of the precipitation comes as snow. In the spring the snow melts causing floods whose timing varies a lot from year to year due to the temperature. There is a significant electricity heating load while the mild summers do not require a lot of air conditioning, so that electricity demand is concentrated on the winter season. The timedependent variation present in the demand results in a seasonal, weekly and daily profile in the electricity spot price and electricity forward curve. However, these price variations are smoothed to some extent in the Nordic market because of the hydropower production. Some hydro producers have the possibility to optimize their discharge up to one year ahead, and many have the possibility for some months ahead. The short-term, i.e. intra-week and intraday, variations in the spot prices decrease due to the easily adjustable hydropower. On the other hand, there is high variation in the price level between different years because the total amount of

On the Term Structure of Interest Rates in the Presence of Reflecting and Absorbing Boundaries

Abstract: To preclude arbitrage, nominal interest rates must remain non-negative. Researchers have captured this feature by modeling the spot rate with volatility structures that vanish as the spot rate tends to zero. However, such volatility structures are in conflict with empirical evidence; volatility can remain relatively large even at low interest rates. In this paper, we investigate the term structure of interest rates for spot rate processes subject to reflecting and absorbing boundaries. Such models preclude negative rates, are consistent with large volatility at low rates, and admit closed form solutions for both bond and European-type derivative security prices. Below, appropriate boundary conditions are derived for spot rates processes that are subject to reflecting and absorbing boundaries. Although it can be demonstrated that spot rate processes with reflecting boundaries can be supported within a general equilibrium framework, we show that reflecting boundaries cannot be placed upon forward rate dynamics without generating arbitrage opportunities. Closed-form bond price solutions for select models are obtained.