Valuation of a spark spread: an LM6000 power plant

Abstract

This paper analyzes a power plant powered by two General Electric LM6000 gas turbines combined with a steam generator that allows combined cycle operations. We consider four distinct operating modes for the plant. Such a plant can be characterized as a real option on a spark spread: optimally converting natural gas to electricity. We use a Margrabe approach by using the market heat rate (the ratio of the electricity price to the natural gas price) as our underlying stochastic variable. We estimate a stochastic model for market heat rates that incorporates time of day, day of week, month, and the incidence or otherwise of a spike in heat rates. We use the model and its residuals in a bootstrap process simulating future market heat rates, and use a least-squares Monte Carlo approach to determine the optimal operating policy. We find that the annual average market heat rate is a good explanatory variable for the time integral of the plant operating margin, denominated in the natural gas numeraire. This allows us to express plant values in terms of the numeraire and convert to dollars by multiplying this by the natural gas forward curve and a forward curve of riskless discount rates. We also provide information about the optimal operating modes selected, the number of transitions between modes and how they relate to transition costs and the average heat rate for the year.

Keywords:

• capital budgeting
• fixed investment and inventory studies contingent pricing
• futures pricing statistical decision theory
• operations research simulation methods

Notes

Since these are changes in the logarithm, a change of −10,000 basis points or −100% does not send the price to zero, but represents a price reduction of over one hour.

Again, since these are logs of prices, the 100% figure in the table is a price increase of .

The Margrabe approach uses a geometric Brownian motion for the ratio of the two prices. In our model, the heat rate ratio will be geometric Brownian motion within each regime, but will jump at each regime-switching point. Thus, it is not a continuous geometric Brownian motion for the whole period. That would present a problem in the European option situations that Margrabe considered, because he used the Black–Scholes model to value the European option to exchange one asset for another. We use LSM techniques to analyze the sequence of American options to switch among operating modes. The LSM approach does not require geometric Brownian motion. Thus, we do not have a strict Margrabe model in our paper, but we continue to use the term in deference to the notion of modeling the ratio of two prices as a univariate stochastic process, rather than the two prices as two separate jointly distributed prices.

The nature of the simulations (and the subsequent valuations) is not affected by the initial market heat rate and day of week because the shocks and seasonality effects have a very short duration. The initial heat rate of 10 is a round number close to the long-run market heat rate of 10.538 reported in Table 1.

Note that the actual ν is used; hence the least-squared technique is only involved in the decisions. A common error is to use νˆ _H−1 which will lead to additional estimation error in the value function.

For example, Table 1 shows the highest standard deviation for 2006.

Indeed, Figure 12 shows that in 2006, the power plant would be at full output 65–75% of the time, depending on the model used, so there would have been little reason to transition the plant to a lower production mode.

Except for the penalty model with the beta being reset each year, and only for the year 2005, where the power generated is quite low. Clearly, the plant is being shut down completely for much of that year.