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Show Results For
- All HBS Web
(839)
- News (77)
- Research (639)
- Events (12)
- Multimedia (4)
- Faculty Publications (635)
- January 2008
- Background Note
Index Options
By: Joshua Coval and Erik Stafford
The goal of this simulation is to understand the patterns in index option prices that are not predicted by the Black-Scholes model. In particular, the simulation focuses on two properties of options prices. First, at-the-money implied volatilities from index options... View Details
Keywords: Volatility; Stock Options; Investment; Price; Profit; Risk Management; Mathematical Methods
Coval, Joshua, and Erik Stafford. "Index Options." Harvard Business School Background Note 208-119, January 2008.
- January 2002 (Revised October 2007)
- Case
Grantham, Mayo, Van Otterloo & Co., 2001
By: Joshua Musher and Andre F. Perold
Asset manager GMO underperforms the market during the 1996-2000 stock market bubble because of the focus on absolute risk. After suffering significant client withdrawals, performance again shines when the bubble collapses. Did they win the battle only to lose the war?... View Details
Keywords: Customers; Asset Management; Stocks; Investment; Price Bubble; Mathematical Methods; Risk and Uncertainty
Musher, Joshua, and Andre F. Perold. "Grantham, Mayo, Van Otterloo & Co., 2001." Harvard Business School Case 202-049, January 2002. (Revised October 2007.)
- October 1993 (Revised August 1996)
- Background Note
Forecasting with Regression Analysis
Provides an example of regression in one of its most important roles. Relating probabilistic forecasts based on past data to decision analysis. View Details
Keywords: Management Analysis, Tools, and Techniques; Analytics and Data Science; Forecasting and Prediction; Mathematical Methods
Schleifer, Arthur, Jr. "Forecasting with Regression Analysis." Harvard Business School Background Note 894-007, October 1993. (Revised August 1996.)
- 12 Feb 2007
- Lessons from the Classroom
‘UpTick’ Brings Wall Street Pressure to Students
upTick." "If it had been a lecture, we would have said what would happen, the students would have nodded, and we would have moved on," adds Stafford. "The theory predicts the endpoint. It doesn't tell you in practice how you're going to get there.... View Details
- 2024
- Working Paper
Pitfalls of Demographic Forecasts of U.S. Elections
By: Richard Calvo, Vincent Pons and Jesse M. Shapiro
Many observers have forecast large partisan shifts in the US electorate based on demographic trends. Such forecasts are appealing because demographic trends are often predictable even over long horizons. We backtest demographic forecasts using data on US elections... View Details
Keywords: Mathematical Methods; Voting; Political Elections; Trends; Forecasting and Prediction; Demographics
Calvo, Richard, Vincent Pons, and Jesse M. Shapiro. "Pitfalls of Demographic Forecasts of U.S. Elections." NBER Working Paper Series, No. 33016, October 2024.
- July 2010 (Revised August 2012)
- Supplement
Assistant Professor Jo Worthington (B)
A professor teaching a case discussion based on numeric analysis is pleased that a student finally "cracks" the case--but the numbers differ from her own. The instructor has to decide how to handle the discrepancy. View Details
Leonard, Dorothy A. "Assistant Professor Jo Worthington (B)." Harvard Business School Supplement 911-405, July 2010. (Revised August 2012.)
- 1979
- Chapter
Research Methods and Data Analysis: The Challenge of Knowing How to Do What About Why
By: T. M. Amabile and W. DeJong
- 2017
- Working Paper
Minimizing Justified Envy in School Choice: The Design of New Orleans' OneApp
By: Atila Abdulkadiroglu, Yeon-Koo Che, Parag A. Pathak, Alvin E. Roth and Oliver Tercieux
In 2012, New Orleans Recovery School District (RSD) became the first U.S. district to unify charter and traditional public school admissions in a single-offer assignment mechanism known as OneApp. The RSD also became the first district to use a mechanism based on Top... View Details
Keywords: Education; Decision Choices and Conditions; Marketplace Matching; Mathematical Methods; Design
Abdulkadiroglu, Atila, Yeon-Koo Che, Parag A. Pathak, Alvin E. Roth, and Oliver Tercieux. "Minimizing Justified Envy in School Choice: The Design of New Orleans' OneApp." NBER Working Paper Series, No. 23265, March 2017.
- Article
Assent-maximizing Social Choice
By: Katherine A. Baldiga and Jerry R. Green
We take a decision theoretic approach to the classic social choice problem, using data on the frequency of choice problems to compute social choice functions. We define a family of social choice rules that depend on the population's preferences and on the probability... View Details
Keywords: Decision Choices and Conditions; Theory; Measurement and Metrics; Mathematical Methods; Society
Baldiga, Katherine A., and Jerry R. Green. "Assent-maximizing Social Choice." Social Choice and Welfare 40, no. 2 (February 2013): 439–460.
- 01 Dec 2008
- News
A U.S. Turnaround?
sad story of our slippage in mathematics and science. In fourth grade, American children are ahead of almost everyone in the world. By the eighth grade they are even, and by twelfth grade they are seriously behind. If you walk through the... View Details
- 01 Feb 1997
- News
Merton Discusses Risk Management at Dean's Seminar
Merton noted that "risk management will become an essential internal process for the lending institution if it expects to remain viable and competitive." By demonstrating mathematically how to determine and hedge risk exposure for any new... View Details
Keywords: Elizabeth McNair
- 1985
- Chapter
The Role of Contingent Claims Analysis in Corporate Finance
By: Scott P. Mason and Robert C. Merton
- 1999
- Chapter
Interest Rate Rules in an Estimated Sticky Price Model
By: Julio J. Rotemberg and Michael Woodford
Rotemberg, Julio J., and Michael Woodford. "Interest Rate Rules in an Estimated Sticky Price Model." In Monetary Policy Rules, edited by John B. Taylor. Chicago: University of Chicago Press, 1999.
- August 2018
- Article
Extrapolation and Bubbles
By: Nicholas Barberis, Robin Greenwood, Lawrence Jin and Andrei Shleifer
We present an extrapolative model of bubbles. In the model, many investors form their demand for a risky asset by weighing two signals: an average of the asset’s past price changes and the asset’s degree of overvaluation. The two signals are in conflict, and investors... View Details
Barberis, Nicholas, Robin Greenwood, Lawrence Jin, and Andrei Shleifer. "Extrapolation and Bubbles." Journal of Financial Economics 129, no. 2 (August 2018): 203–227.
- 2016
- Working Paper
Algorithmic Foundations for Business Strategy
By: Mihnea Moldoveanu
I introduce algorithmic and meta-algorithmic models for the study of strategic problem solving, aimed at illuminating the processes and procedures by which strategic managers and firms deal with complex problems. These models allow us to explore the relationship... View Details
Moldoveanu, Mihnea. "Algorithmic Foundations for Business Strategy." Harvard Business School Working Paper, No. 17-036, October 2016.
- 1995
- Book
Introduction to Statistical Decision Theory
By: John W. Pratt, Howard Raiffa and Robert Schlaifer
Pratt, John W., Howard Raiffa, and Robert Schlaifer. Introduction to Statistical Decision Theory. MIT Press, 1995.
- January 1990 (Revised February 1990)
- Case
MSA: The Software Company--Planning the AMAPs Product Line
By: Robert J. Dolan
MSA has commissioned a major market research study to assess demand potential for a computer software system designed for aerospace and defense contractors. Students must evaluate the results of the study (including a conjoint analysis) to assess whether MSA should... View Details
Dolan, Robert J. "MSA: The Software Company--Planning the AMAPs Product Line." Harvard Business School Case 590-069, January 1990. (Revised February 1990.)
- May 1984 (Revised September 1986)
- Background Note
Basic Quantitative Analysis for Marketing
By: Robert J. Dolan
Shows how to calculate and use the break-even volume in marketing decision making. View Details
Dolan, Robert J. "Basic Quantitative Analysis for Marketing." Harvard Business School Background Note 584-149, May 1984. (Revised September 1986.)
- 2022
- Article
Which Explanation Should I Choose? A Function Approximation Perspective to Characterizing Post hoc Explanations
By: Tessa Han, Suraj Srinivas and Himabindu Lakkaraju
A critical problem in the field of post hoc explainability is the lack of a common foundational goal among methods. For example, some methods are motivated by function approximation, some by game theoretic notions, and some by obtaining clean visualizations. This... View Details
Han, Tessa, Suraj Srinivas, and Himabindu Lakkaraju. "Which Explanation Should I Choose? A Function Approximation Perspective to Characterizing Post hoc Explanations." Advances in Neural Information Processing Systems (NeurIPS) (2022). (Best Paper Award, International Conference on Machine Learning (ICML) Workshop on Interpretable ML in Healthcare.)
- 2022
- Article
Fairness via Explanation Quality: Evaluating Disparities in the Quality of Post hoc Explanations
By: Jessica Dai, Sohini Upadhyay, Ulrich Aivodji, Stephen Bach and Himabindu Lakkaraju
As post hoc explanation methods are increasingly being leveraged to explain complex models in high-stakes settings, it becomes critical to ensure that the quality of the resulting explanations is consistently high across all subgroups of a population. For instance, it... View Details
Dai, Jessica, Sohini Upadhyay, Ulrich Aivodji, Stephen Bach, and Himabindu Lakkaraju. "Fairness via Explanation Quality: Evaluating Disparities in the Quality of Post hoc Explanations." Proceedings of the AAAI/ACM Conference on Artificial Intelligence, Ethics, and Society (2022): 203–214.