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Three-Dimensional Price Forecasting

Using the past, present, and future to optimize our understanding of today’s energy markets.
Fortnightly Magazine - April 2007

to these attributes as volatility and correlation. These are the second and third dimensions of the price-forecasting process.

Analysts must feel free to rely upon fundamentalists or econometricians to generate the expected forecast as always. But beyond that, they should demand a reflection of uncertainty around that number. In addition, there is no market more interrelated than the natural-gas and power markets. Therefore, correlation is equally important. In fact, most gas trading activity is quoted and transacted in a “basis” context rather than “flat price.” This means that one must fully understand the relationship between whatever location he or she are trading in and the flat price location (Henry Hub in many cases). Similarly, in power, we often have liquid traded regional locations and many less liquid, nodal locations where differentials to that liquid market are the only trades available.

Three-dimensional pricing incorporates explicit point forecasts with measures of uncertainty and correlation.

Consider an example. Path-dependent Monte Carlo simulations can incorporate the expected forecasts for each market and build a distribution around them that reflects each market’s volatility and the correlation between each market. Imagine creating a thousand unique price paths for all of the markets relevant to your business. What does this look like?

Suppose forecasting groups apply their fundamental and econometric methods to come up with a consensus six-month forecast of PJM on peak prices. Table 1 summarizes this forecast at the monthly level.

A number of analytic methods are available to generate distributions around this forecast at an hourly, daily, or monthly level. These distributions describe the level of uncertainty the organization has on its forecast. Table 2 illustrates the set of data that would be generated using a path-dependent Monte Carlo price simulator that generates 1,000 price paths of PJM on-peak prices beginning Jan. 1 and moving through June 30, 2007.

One can see that on any day, across the 1,000 iterations, the simulated price varies. Some prices are much higher than the forecast while others are much lower. This information can be summarized and the distribution described simply as a range of prices given some probability. Table 3 summarizes the distribution of prices for May 2007.

By incorporating this uncertainty around the forecast, the analyst now can wrap a range of values around the forecast. Instead of simply indicating that the PJM on-peak spot price is expected to be $61.76/MWh, the analyst also can indicate that he or she is 95 percent certain that the actual number will be above $40.91/MWh. The analyst also can indicate that he or she is 95 percent certain that the actual price will be below $90.30/MWh. This range of value is invaluable for trade pricing, risk measurement, and portfolio optimization.

However, we have not yet identified the third dimension. Correlation between market factors is as important as volatility when dealing with issues that are dependent on more than one market factor.

Suppose the organization wishes to value a 6-month natural-gas-fired tolling contract in PJM. This contract is priced on PJM on- and off-peak prices plus natural-gas prices at Henry Hub. The