Switch, Switch, Switch! A Regime-Switching Option-Based Model for Valuing a Tolling Agreement

Abstract

This article proposes a real options valuation of a tolling contract using a combined switching option and volatility regime switching model. In a tolling-based transaction, the toller becomes the energy manager (but not the owner) of the power plant, having the option to switch it on or off to benefit from (mitigate) the upside (downside) potential related to frequent, jumpy fluctuations of power (and gas) prices. Value creation from such flexibility in managing the spark spread risk may be better captured by expanding the static NPV of the plant via exercise of a switching (compound) option having the plant itself as an underlying two-market-based asset portfolio (electricity and gas). Results from adoption of a pentanomial lattice pricing approach show that the set of tolling fees the toller would prefer to pay to the tollee “in equilibrium” is a decreasing function in the portfolio volatility because of the higher risk being borne by the former. Though the toller is willing to fairly pay equal or less than the value created from active management of the power plant, obtaining a positive net profit, the tollee may rely on a constant flow of bullet bond-like installments, securing remuneration of equity capital invested and arrangement of a project financing for plant construction.

Notes

Moel and Tufano (2002) conducted an empirical study of the set of predictions derived from Brennan and Schwartz (1985b) on decision rules governing gold mine openings and closings using a probit multivariate discrete choice model. In this sense, our real options model is close in spirit to what was empirically tested by these two authors. Because the power plant underlying the tolling agreement is more likely to be switched on if the level of electricity prices and their volatility increase, so Moel and Tufano similarly showed that the probability of a mine being open increases with an increase in gold price and its volatility (as well as with the observation of a prior opening state for the mine).

Peak hours range from 8:00 a.m. to 8:00 p.m. and off-peak hours are represented by the late night and early morning hours (8:00 p.m. to 7:00 a.m.).

Typically, the geometric Brownian motion (GBM) is extended to take these features into account. Mean reversion is typically modeled by means of a drift term ([]) that is negative if the spot price () is higher than the mean reversion level () and positive if the spot price is lower than the mean reversion level. The speed of mean reversion () determines how fast the price will revert to its mean level. Jumps are accounted for by two additional variables: , the frequency of jumps, and v, a random variable describing the severity of each jump. In particular, modeling the jump feature with a Poisson process has become the industry standard. Empirical studies show that the electricity price is rapidly forced back to its mean level after a jump. In this sense, it may be interesting to have a process where a positive jump is always (or likely to be) followed by a negative jump to capture the rapid decline of power prices after a spike. The GBM used as a benchmark for modeling electricity prices is the following:

Expectations over the next-period payoffs are formulated under the risk-neutral probability measure.

u, d, and m stand for up, down, and middle, respectively. J and NJ stand for jump and no-jump regime, respectively. is the net present value of the power plant as managed by the toller at time t and state s when operating in mode m (also called NPV₂).

In contrast to what Deng and Xia (2006) have developed in their model, when there are costs associated with switching from the on mode to the off mode and vice versa, simply adding up separate spark-spread options would not yield the total value of flexibility resulting from active plant management. This is due to the fact that those options would no longer be independent. Hence, the presence of switching costs may break the additivity link existing among single spark-spread options and generate option compoundness.

SPE directly owns 1,593 MW (10%) and Electrabel 13,127 MW (81%) of the overall installed capacity. The market share of other independent generators is limited (1,403 MW) and distributed across smaller units.

CCGT operators may benefit from the actions of Electrabel (the sole incumbent) to securitize a minimum return on investments.

The technical features of the power plant are gross power plant output (415 MW); net plant power output (408 MW); gross plant efficiency (57.4%); net plant efficiency (56.4%).

A straight-line depreciation method is applied with a rate of 8%.

The cost of equity is 10.1% (also coinciding with the internal rate of return), the cost of debt is 6.1%, and the tax rate is 33.99%.

The Consumer Price Index used for inflation adjustment is equal to 1.9%.

From the tollee's standpoint, the plant switching only impacts maintenance operations, whose expenses are covered by the incoming tolling fee.

SMaPS, which stands for spot market price simulator, is a stochastic three-factor model for hourly spot prices of electricity in deregulated markets. Such a model has been jointly developed by EnBW (Germany's third-largest energy company) and the University of Karlsruhe (see Burger et al. 2004). The fundamental equation of the SMaPs model is

where:

= electricity load observable by market participants (demand);

= expected relative availability of power plants;

= residual short-term market fluctuations due to the “psychology of the market”;

= stochastic process (random walk with drift) accounting for the long-term variation of futures prices (that cannot be estimated from historical data of the spot market).

This means that f is an empirically estimated price load curve also incorporating the technicalities of electricity production reflected in the ratio , called adjusted load.

The annual weighted average cost of switching is computed as follows:

€32.290 and €8.072 are the unit costs of startup and shut-down as computed by taking the 80 and 20% of €40.363, respectively. If they are multiplied by 106, total annual startup and shut-down costs are alternatively obtained.

The scale factor is determined as follows: • The weighted average annual peak over off-peak power price is

• The weighted average annual cost of gas (peak) is

As for the heat rate (6.38) is replaced by (6.76), max capacity (408 MW) by min capacity (245 MW), and total peak hours per year (4345) by total off-peak hours (1485).

If the full set of dynamic tolling fees with no inflation adjustment (from 2017 onwards) is applied, the tollee's NPV is €64.99 million and the toller's NPV is -€6.72 million. The latter figure may urge the toller to consider the dynamic tolling fee as an ultimate cap and attempt to negotiate a lower set of payment installments from the LT year 2021 onwards (e.g., replacing the residual set of fees with the inflation-adjusted one would yield a €15.85 million NPV). If the set of dynamic tolling fees with inflation adjustment at 1.9% (from 2017 onwards) is applied, the tollee's NPV is €19.10 million and the toller's NPV is €21.41 million.