Credit Value Adjusted Real Options Based Valuation of Multiple-Exercise Government Guarantees ...

153 Pages·2011·0.47 MB·English

Credit Value Adjusted Real Options Based Valuation of
Multiple-Exercise Government Guarantees for
Infrastructure Projects

By

Ali Naji Almassi

A thesis submitted in conformity with the requirements
for the degree of Doctor of Philosophy

The Department of Civil Engineering
The University of Toronto
Toronto, Ontario

© Copyright by Ali Naji Almassi (2011)
ABSTRACT

Credit Value Adjusted Real Options Based Valuation of Multiple-
Exercise Government Guarantees for Infrastructure Projects

Ali Naji Almassi

Doctor of Philosophy
The Department of Civil Engineering
The University of Toronto
2011

Public-Private-Partnership (P3) is gaining momentum as the delivery method for the
development of public infrastructure. These projects, however, are exposed to economic
risks. If the private parties are not comfortable with the level of the risks, they would not
participate in the project and, as a result, the infrastructure will most likely not be
realized. As an incentive for participation in the P3 project, private parties are sometimes
offered guarantees against unfavorable economic risks. Therefore, the valuation of these
guarantees is essential for deciding whether or not to participate in the project.

While previous works focused on the valuation of guarantees, the incorporation of credit
risk in the value of the P3 projects and the guarantees has been neglected. The effect of
credit risk can be taken into account by using the rigorous Credit Value Adjustment
method (CVA). CVA is a computationally demanding method that the valuation methods
currently in the literature are not capable of handling.
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This research offers a novel approach for the valuation of guarantees and P3 projects
which is computationally superior to the existing methods. Because of this computational
efficiency, CVA can be implemented to account for credit risk. For the development of
this method, a continuous stochastic differential equation (SDE) is derived from the
forecasted curve of an economic risk. Using the SDE, the partial differential equation
(PDE) governing the value of the guarantees will be derived. Then, the PDE will be
solved using Finite Difference Method (FDM). A new feature for this method is that it
obtains exercise strategies for the Australian guarantees.

The present work extends the literature by providing a valuation method for the cases that
multiple risks affect P3 projects. It also presents an approach for the valuation of the
Asian style guarantee, a contract which reimburses the private party based on the average
of risk factor. Finally, a hypothetical case study illustrates the implementation of the
FDM-based valuation method and CVA to obtain the value of the P3 project and the
guarantees adjusted for the counterparty credit risk.

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ACKNOWLEDGMENTS

I would like to express my deepest gratitude and sincere appreciation to my supervisor
and mentor, Professor Brenda McCabe, for her continuous support, encouragement, and
guidance throughout the course of my study at the University of Toronto. Her open-
mindedness and flexibility created a free research environment which made my years at
the University of Toronto a memorable journey. I also owe her very much gratitude for
being always available when I needed her insightful advice. I am truly honored that
Professor McCabe is my “academic parent”.

I am greatly thankful to my co-advisor at Queen’s University, Professor Matthew
Thompson, for his devotion and invaluable guidance during all phases of this research. I
am grateful for the many challenging and thought-provoking discussions we had. I
enjoyed every single one of them as they not only helped me in my research, but also
influenced my professional life. It was an incredible opportunity to not only meet
Professor Thompson, but also to work under his guidance. I hope we continue our
academic collaboration in future.

I would like to sincerely thank Professor Joseph Paradi and Professor Kim Pressnail, my
advisory committee members, whose critical comments enriched this research. I would
also like to acknowledge Professor Matt Davison, the external examiner, for his
constructive comments. I am indebted to all of them for their contributions and thought-
stimulating questions.
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My thanks go to all my professors at the University of Toronto, Queen’s University, and
Sharif University of Technology. I am indebted to all of them for educating me in all
these years. I would like to thank all my friends at the University of Toronto who made
this experience much more rewarding than I ever thought it could be.

Last but not least, I extend my deepest gratitude and sincere thanks to my dearest parents
to whom this work is dedicated for their endless love and self-devotion and my beloved
sister, Sara, for her belief and unconditional support. They have been a constant source of
encouragement in my academic endeavors and will continue to be my inspiration in life.

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To my beloved parents

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TABLE OF CONTENTS

Chapter 1 Introduction.....................................................................................................1
1.1 Background.........................................................................................................1
1.2 BOT Project Risk................................................................................................4
1.3 The Importance of Government Guarantees Valuation......................................6
1.4 Government Guarantee Structure.......................................................................7
1.5 Valuation Models of Government Guarantees...................................................8
1.6 Motivations and Objectives..............................................................................10
1.7 General Research Approach.............................................................................13
1.8 Scope and Limitation........................................................................................14

Chapter 2 Literature Review..........................................................................................16
2.1 Background.......................................................................................................16
2.1.1 Public-Private-Partnership Background....................................................16
2.1.2 BOT Framework.......................................................................................16
2.1.3 Advantages of BOT..................................................................................18
2.2 BOT Risks.........................................................................................................19
2.3 Government Supports.......................................................................................20
2.4 Government Guarantees....................................................................................22
2.5 Real Option.......................................................................................................24
2.5.1 Applications of Real Options in Civil Engineering..................................25
2.5.2 Risk Modeling in BOT Projects................................................................26
2.6 Government Guarantee Framework..................................................................30
2.7 Guarantees on Average Risk Value..................................................................32
2.8 Credit Risk Consideration.................................................................................32

Chapter 3 Risk Modeling...............................................................................................34
3.1 Background.......................................................................................................34
3.2 The Continuous Model.....................................................................................36

Chapter 4 Explicit Finite Difference Method for one-factor models............................39
4.1 Background.......................................................................................................39
4.2 PDE Derivation.................................................................................................39
4.3 Finite Difference Method (FDM).....................................................................43
4.4 FDM Implementation for Government Guarantee...........................................47
4.5 Deriving Exercise Strategies for Australian Guarantees..................................53
4.6 Verifying Exercise Strategies by Simulation....................................................55
4.7 Numerical Example..........................................................................................56
4.8 Estimation of the Probability of a Budget Shortfall..........................................60

Chapter 5 Explicit Finite Difference Method for Two-Factor Models.........................65
5.1 Background.......................................................................................................65
5.2 The SDE for Short-term Interest Rate..............................................................65
5.3 PDE Derivation.................................................................................................66
5.4 FDM Implementation for Government Guarantee...........................................70
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5.5 Exercise Strategies for Guarantees under Two Sources of Uncertainty...........79
5.6 Verifying Exercise Strategies by Simulation....................................................80
5.7 Multiquadric Radial Basis Functions................................................................82
5.8 Numerical Example..........................................................................................83

Chapter 6 Asian Style Guarantee...................................................................................86
6.1 Background.......................................................................................................86
6.2 PDE Derivation.................................................................................................86
6.3 Approaches for Solving Asian option PDEs.....................................................90
6.4 FDM Implementation for the Asian-Style Government Guarantee..................92
6.5 Exercise Strategies for Guarantees with the Asian-Style Payoff....................104
6.6 Verifying Exercise Strategies by Simulation..................................................105

Chapter 7 Credit Value Adjustment............................................................................107
7.1 Background.....................................................................................................107
7.2 Credit Value Adjustment (CVA)....................................................................109
7.3 Credit Risk in BOT Projects...........................................................................111
7.4 Credit Value Adjustment in Australian Guarantee Contracts.........................112
7.5 FDM vs. LSM for CVA Calculation...............................................................114
7.6 Credit Value Adjustment for the Loan Contract.............................................115
7.7 PDE Derivation...............................................................................................116
7.8 Solving the PDE..............................................................................................120
7.9 CVA Implementation for Loan.......................................................................125

Chapter 8 Hypothetical Example.................................................................................127

Chapter 9 Conclusions and Recommendations...........................................................132
9.1 Conclusion......................................................................................................132
9.2 Summary of the Contributions........................................................................133
9.3 Recommendations for Future Research..........................................................134

References:......................................................................................................................135

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LIST OF FIGURES

Figure 1-1: BOT Delivery Method.....................................................................................................3
Figure 2-1: Contracts between the Project Company and the Stakeholders.....................................18
Figure 2-2: BOT Risks (after Dailami et al. 1999 and Chiara 2006)................................................20
Figure 4-1: Illustration of Finite Difference Method for an Option Contract...................................44
Figure 4-2: Illustration of Finite Difference Method for Government Guarantee............................48
Figure 4-3: Identify 2 Nearest Grid-points.......................................................................................53
Figure 4-4: Forecasted Curve of R...................................................................................................57
Figure 4-5: Comparing Values of Australian Guarantees Obtained From LSM and FDM..............59
Figure 4-6: Comparing Values of Australian Guarantees Obtained From ESR and FDM...............60
Figure 4-7: Comparing the Realized and Theoretical Probabilities of Budget Shortfall..................64
Figure 5-1: Illustration of FDM for Government Guarantee with Stochastic Z=ln(R) and =ln(r).72
Figure 5-2: Illustration of 4 Nearest Gridpoints in Two-dimensional FDM....................................78
Figure 5-3: Illustration of Bilinear Interpolation for Two-dimensional FDM..................................79
Figure 5-4: Comparing Values of Australian Guarantees Obtained From FDM and MQRB..........84
Figure 5-5: Comparing Values of Australian Guarantees Obtained From FDM and ESR...............85
Figure 6-1: Illustration of The PDE Discretization in A and Z Direction........................................94
Figure 6-2: Illustration of 4 Nearest Gridpoints in Guarantees with the Asian-Style Payoff.........103
Figure 6-3: Illustration of Bilinear Interpolation............................................................................104
Figure 8-1: Equity Value of the Project with Different Number of Granted Guarantees...............130

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LIST OF TABLES

Table 4-1: Forecasted Values of R at the End of Each Year.........................................................58
Table 4-2 Comparing Values of Australian Guarantees Obtained From LSM and FDM.............58
Table 4-3: Comparing Values of Australian Guarantees Obtained From FDM and ESR.............60
Table 5-1: Comparing Values of Australian Guarantees Obtained From FDM and MQRB........84
Table 5-2 Comparing Values of Australian Guarantees Obtained From FDM and ESR..............85
Table 7-1: A BOT Project Economic Balance Sheet..................................................................115
Table 8-1: Traffic Demand and Financial Projection for the Project..........................................129
Table 8-2: Equity Value of the Project with Different Number of Granted Guarantees.............129
Table 8-3: Present Value of the Loan Adjusted for Credit Risk..................................................131

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