Gordon Sick, Professor of Finance, U of Calgary

Real Options Tutorial

These are slides for a talk that I gave at the Multinational Financial Society Conference in Orlando on July 28, 2008. Here are the movies for the Kalman filter models of crude oil and natural gas.

Valuation of a Spark Spread: an LM6000 Power Plant

This paper analyzes a power plant in Alberta, Canada, that is powered by two General Electric LM6000 gas turbines combined with a steam generator that allows combined cycle operations. The LM6000 is derived from a GE engine used on Boeing 767 and 747 airplanes, and is adapted for natural gas by General Electric. This power plant is popular in various power jurisdictions around the world as a turnkey power plant that can offer peaking capacity, and some baseload power delivery.

We consider 4 operating modes for the plant: cold metal (off), 15 MW idle in com- bined cycle, full simple-cycle power (95 MW) and combined cycle full power (120 MW).

It is common to refer to such a plant as generating a spark spread: converting natural gas to electricity by burning. A spark spread has two correlated stochastic variables: electricity price and natural gas price. To lower the dimensionality of the problem, we worked with heat rates. The market heat rate is the ratio of the electricity price to the natural gas price and the plant heat rate is the number of gigajoules (GJ) of gas needed to generate one MWh of electric power. This allows us to analyze the problem using the Margrabe approach, using natural gas as the numeraire commodity.

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.

Real Options and Regulation

These are slides for a talk I gave at the Melbourne Financial Centre on January 23, 2008. They explore several issues that arise when an entity with real options is subject to economic regulation. I argue that the service provider should be able to recover compensation for the opportunity cost of real options it extinguished to create the regulated capital asset. I also show that single-part tariffs in facilities access regulation distort the incentives of the access provider (to underprovide excess capacity) and of the access seeker (to demand too much excess capacity).

This talk has morphed into a more complete paper and slides with the following abstract:

In this paper, we investigate optimal tariffs for facilities access when the facility Builder has a real option to choose the optimal timing of construction. Pindyck (2004, 2005) suggests that the cost base for a regulated access tariff should include actual out-of- pocket costs of the facilities Builder plus the value of real options that are extinguished by committing capital and building. Pindyck suggests that not allowing for a recovery of the real option value will distort the ex ante incentives of the facilities Builder and not result in a first-best solution. However, he focuses on the analysis of a one-part tariff that would recover the total cost (capital plus option opportunity cost) without analyzing the nature (social cost, change in investment timing) of the distortions from various tariff policies. His one-part tariff would be an annual charge to recover capital cost plus real option value extinguished. But, he does not consider the possibility of a two-part tariff to mitigate all of these distortions. If an access Seeker is allowed to enter and then abandon, they have a free call option on the facility, but an annual tariff does not provide appropriate incentive to use this option as if they were the Builder. Thus, in addition to an annual tariff, it is necessary to charge an up-front fee to make this option costly. The fee resembles the capital cost of building, which is incurred by the Builder. This suggests that a two-part tariff is needed to attain social optimality.
This paper analyzes those possibilities.
We use a methodology for analyzing entry and exit options from Dixit et al. (1999); Sødal (2006) to analyze this model.

Research Working Papers

This paper addresses a common problem in the petroleum industry, using techniques of real options in a cooperative game setting. It has the added twist of a network effect that encourages early development. In the model, two natural gas producers have adjacent undeveloped land with uncertain reserves. They must decide when to develop (drill and connect) their fields. In addition, one or both of them must build a gas processing plant to remove corrosive and toxic impurities, to make the gas suitable for entering a pipeline. Then, they must induce a pipeline company to build a gathering system to take their gas to market.

There is a real option for both producers to delay until they have suitable price and reserves conditions. But, there are incentives to be the first mover who can also build a gas plant to its own specifications and locational preference. This gives a first mover advantage that encourages early development. Also, there is a beneficial network effect from encouraging the follower to enter immediately and reduce the unit toll cost needed to induce the pipeline builder to enter. Thus, the first mover has to decide when to build, what capacity to build and what processing lease rate to offer the second mover. We believe that the problem is more general than the specific petroleum industry problem we model, insofar as it reflects a combination of real option theory to develop, coupled with competitive game theory between a leader and a follower in the development of a common-use asset and cooperative game theory between the leader and the follower to capture a network effect.

Investment under Uncertainty, Debt and Taxes
Andrea Gamba Department of Economics, University of Verona, Verona, Italy
Gordon A. Sick, Haskayne School of Business, University of Calgary
Carmen Aranda Leon, University of Navarra, Pamplona, Spain.

Abstract:
We present a capital budgeting valuation framework that takes into account both personal and corporate taxation. We show broad circumstances under which taxes do not affect the martingale expectations operator. That is, the martingale operator is the same before and after personal taxes, which we call "valuation neutrality".

The appropriate discount rate for riskless equity-financed flows (martingale expectations or certainty-equivalents) is an equity rate that differs from the riskless debt rate by a tax wedge. This tax wedge factor is the after-tax retention rate for the corporate tax rate that corresponds to tax neutrality in the Miller equilibrium. We extend this result to the valuation of the interest tax shield for exogenous debt policy with default risk. Interest tax shields accrue at a net rate corresponding to the difference between the corporate tax rate that will be faced by the project and the Miller equilibrium tax rate. Depending on the financing system, interest tax shields can be incorporated by using a tax-adjusted discount rate or by implementing an APV-like approach with additive interest tax shields.

We also provide an illustrative real options application of our valuation approach to the case of an option to delay investment in a project, showing that the application of Black and Scholes formula may be incorrect in presence of personal and corporate taxes.

Keywords: Investment under uncertainty, real options, capital structure, risk-neutral valuation, corporate and personal taxation, default risk, interest tax shields, cost of capital, tax-adjusted discount rates

Modelling Electricity Price Risk
Robert Elliott, Gordon Sick and Michael Stein
Abstract:
In this paper we develop a general model of spot electricity price that encom- passes the stylized features of many of the emerging deregulated electricity pools around the world.

We incorporate seasonality on an annual basis and a daily basis around a mean-reverting de-seasonalized intrinsic price. A unique feature of this paper is the treatment of jumps in the spot price as arising from supply shocks as large generators in the system come off-line and go on-line in a partially predictable manner. We model the number of large generators on line as a discrete Markov process.

This feature is motivated by the Alberta electricity pool,which has 14 large base-load generators and very little excess capacity. We show how to estimate the diffusion process with a Kalman filter technique and the discrete Markov model with maximum likelihood model. The motivation for pricing calls on this price process is two-fold.First many electricity customers purchase call options to manage their risk.Sec- ond,generators are called into the system or turned on, according to whether their marginal price is less than or greater than the system marginal price (spot price).The revenue stream to a company that builds a new generator that is not part of base load will be a strip of call options.Thus,this is a real option valuation model.

Abstract:
This paper explores real options methodology as a risk management tool. In- stead of characterizing the value of a real option to an organization as some potentially unrealizable notional market value, it characterizes the real option as a tool for mitigating downside risk while allowing most of the upside potential of a project to flow through to its owner. We do this by simulating the value generated by a real option strategy and comparing it to the alternative strategies of immediate development (based on the NPV rule) and delay as long as possible (generating a european call option). We compare the cumulative distributions of simulated value for the three strategies and compare them by means of total dominance, and second degree stochastic dominance. Real options do not totally dominate, nor do they always dominate the other two strategies in the second degree. However, the analyst can examine the graphs of the cumulative distributions to see what sort of risk- averse utility function would be needed to justify a preference of one of the alternatives to a real option strategy. The simulations are performed both for a risk-neutral distribution and for a risk-averse distribution. The distributions differ from each other by a risk premium in the drift of underlying asset value. Strictly speaking, stochastic dominance analysis should be performed on the true (risk-averse) distribution, rather than the risk-neutral distribution. Thus, dominance analysis performed on the risk-neutral distribution implicitly assumes there is no risk premium.

Gordon Sick

Presentations

Real Options Tutorial

Valuation of a Spark Spread: an LM6000 Power Plant

Real Options and Regulation

Research Working Papers

Forthcoming Paper