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 futures prices and natural gas futures. I did this work with my colleague Mark Cassano.

We also have a Kalman filter model of copper futures prices, with a movie of the dynamics. It is interesting to note that the crude oil and copper futures models have structural breaks, where the normally quiet long-term factor explodes upward. The break in crude oil occurs in 2003-2004, but the copper break occurs in 2006.

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).

Forthcoming Paper

Some Important Issues Involving Real Options: An Overview
Andrea Gamba Department of Economics, University of Verona, Verona, Italy
Gordon A. Sick, Haskayne School of Business, University of Calgary

Multinational Finance Journal.
http://www.mfsociety.org/page.php?pageID=175&reqJournInstID=36

Abstract
This paper provides an introduction to real options, as well as highlighting some important issues that are often neglected by real options analysts. While many books and surveys have been written on real options, there are some ubiquitous concepts that are not well-understood by many authors and practitioners. The objective of this paper is to redress this shortfall. The paper discusses organizational issues that impede adoption of real options strategies. It discusses modelling and analytic techniques for real options.

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

Forthcoming Paper

Research Working Papers