Published Nov 25, 2022
This course considers the application of option concepts from finance to value real assets. The focus is on using real options theory and methodology to value investments characterized by uncertainty, irreversibility, and flexibility in the timing of irreversible expenditures. The course begins with an introduction to stochastic processes, Ito's Lemma, the Black-Scholes equation, contingent claims analysis and dynamic programming. Methods to solve simple option value problems will be presented, such as binomial trees and Monte Carlo simulation. Applications will focus on problems in natural resource and environmental economics, such as valuing the option to drill for oil or install pollution control equipment and, time permitting, other applications in economics.
Knowledge of microeconomic theory, basic calculus and linear algebra and some experience with differential equations are required. Assignments require some programming in Matlab, which students are expected to learn on their own. Alternatively, with the approval of the instructor, students may use an alternative programming language of their choice, such as R or Python. Please contact the instructor if you wish to use something other than Matlab.
| Explain why and how uncertainty and irreversibility affect a firm's optimal investment decisions. |
| Explain the analogy between financial options and a firm's decision to undertake capital investment, and describe how real options analysis fits into the broader topic of investment under uncertainty. |
| Explain key building blocks for valuing investment under uncertainty including stochastic differential equations, dynamic programming, Hamilton-Jacobi-Bellman equations, and risk neutral valuation. |
| Analyze simple problems of investment under uncertainty, determining a closed form solution if available or using a simple numerical technique. |
| Read and critique a relevant academic paper, and present a summary of the paper's motivation and results to an audience of the student's peers. |
(Assignment 1 due on Feb 2)
| Title / Name | Notes / Comments | Required |
|---|---|---|
| Dixit and R. Pindyck, (1994) Investment under Uncertainty, Princeton University Press. | Available through the library | Yes |
| Hull, John C. (2006) Options, Futures, and Other Derivatives, Pearson, Prentice, Hall. | Many editions of this book are available. Provides a useful introduction to financial options. | No |
| Neftci, Salih N. (2000), An Introduction to the Mathematics of Financial Derivatives, second edition, Academic Press. | A useful reference | No |
| Ross, Sheldon M. (1999) An Introduction to Mathematical Finance: Options and Other Topics, Cambridge University Press. | A useful reference | No |
| Component | Value |
|---|---|
| Assignment 1 (Due Thurs Feb 2) | 10% |
| Midterm (In class, Tuesday Feb 14) | 20% |
| Assignment 2 (Due Tues March 14) | 10% |
| Project (Project writeup due Thurs April 6) | 20% |
| Final exam (Date to be determined) | 40% |
No assignment screening will be used in this course.
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