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  • All HBS Web  (575)
    • News  (74)
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  • April 1986 (Revised May 1996)
  • Background Note

Note on Option Pricing

Develops a simple option pricing model which provides an insight into the foundations of the Black and Scholes model. The Black and Scholes model is next introduced and its relationship to the simple option pricing model discussed. Last, the problem of pricing debt... View Details
Keywords: Price; Capital Markets
Citation
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Mason, Scott P. "Note on Option Pricing." Harvard Business School Background Note 286-112, April 1986. (Revised May 1996.)
  • January 2016 (Revised April 2017)
  • Case

The Galaxy Dividend Income Growth Fund's Option Investment Strategies

By: W. Carl Kester
This case is designed to provide an elementary introduction to options and option pricing for beginning finance students. Analysis of the case requires students to compare the prices of put and call options with various exercise prices and maturity dates on two... View Details
Keywords: Options; Option Contract; Option Pricing; Derivatives; Mutual Funds; Call Options; Put Options; Stock Options; Risk and Uncertainty; Volatility; Financial Services Industry; United States
Citation
Educators
Purchase
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Kester, W. Carl. "The Galaxy Dividend Income Growth Fund's Option Investment Strategies." Harvard Business School Case 216-041, January 2016. (Revised April 2017.)
  • September 1997 (Revised February 2000)
  • Exercise

Exercises in Option Pricing and Real Option Analysis

By: Benjamin C. Esty
Contains five problems, one each on basic option pricing, abandonment value, the value of waiting to invest, contingent claims analysis (equity as a call option), and strategic decision making in an option framework. The goal is for students to recognize option value... View Details
Keywords: Stock Options; Price
Citation
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Esty, Benjamin C. "Exercises in Option Pricing and Real Option Analysis." Harvard Business School Exercise 298-053, September 1997. (Revised February 2000.)
  • November 2016 (Revised November 2016)
  • Supplement

The Galaxy Dividend Income Growth Fund's Option Investment Strategies

By: W. Carl Kester
Keywords: Options; Option Contract; Option Pricing; Derivatives; Mutual Funds; Call Options; Put Options; Stock Options; Risk and Uncertainty; Volatility; Financial Services Industry; United States
Citation
Purchase
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Kester, W. Carl. "The Galaxy Dividend Income Growth Fund's Option Investment Strategies." Harvard Business School Spreadsheet Supplement 217-703, November 2016. (Revised November 2016.)
  • spring 1973
  • Article

Theory of Rational Option Pricing

By: Robert C. Merton
Keywords: Theory; Price
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Merton, Robert C. "Theory of Rational Option Pricing." Bell Journal of Economics and Management Science 4, no. 1 (spring 1973): 141–183. (Chapter 8 in Continuous-Time Finance.)
  • November 1984
  • Background Note

Black-Scholes Option Pricing Program for the HP 12C Calculator

By: Andre F. Perold
Contains a program that can be used on the HP12C pocket calculator to compute the Black-Scholes option price and the associated hedge ratio. The program must be given the following parameters: the exercise price, the risk-free rate, the time to expiration, and the... View Details
Keywords: Stock Options; Investment Funds; Price; Management; Software
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Perold, Andre F. "Black-Scholes Option Pricing Program for the HP 12C Calculator." Harvard Business School Background Note 285-057, November 1984.
  • January–February 2020
  • Article

Consumer Reactions to Drip Pricing

By: Shelle Santana, Steven Dallas and Vicki Morwitz
This research examines how drip pricing—a strategy whereby a firm advertises only part of a product’s price upfront and then reveals additional mandatory or optional fees/surcharges as the consumer proceeds through the buying process—affects consumer choice and... View Details
Keywords: Drip Pricing; Pricing; Consumer Protection; Hidden Fees; Price; Consumer Behavior; Perception
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Santana, Shelle, Steven Dallas, and Vicki Morwitz. "Consumer Reactions to Drip Pricing." Marketing Science 39, no. 1 (January–February 2020): 188–210.
  • May 2000
  • Article

Optimal Exercise Prices for Executive Stock Options

By: Brian Hall
Keywords: Management; Stock Options
Citation
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Hall, Brian. "Optimal Exercise Prices for Executive Stock Options." American Economic Review 90, no. 2 (May 2000).
  • September 2, 2020
  • Article

How to Pay for Public Option Without Tax Hike

By: Regina E. Herzlinger and Richard Boxer
A bipartisan combination of the two parties’ most popular initiatives can expand health care coverage, significantly reduce costs, and enable freedom of choice, without raising taxes. Along the way, we can revitalize competition between public and private plans. Our... View Details
Keywords: Health Insurance; Public Option; Health Care and Treatment; Insurance; Cost Management; United States
Citation
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Herzlinger, Regina E., and Richard Boxer. "How to Pay for Public Option Without Tax Hike." RealClearPolicy (September 2, 2020).
  • October 2004
  • Article

Demand for Portfolio Insurance and Index Option Prices

By: Kaushik Amin, Joshua D. Coval and H. Nejat Seyhun
Keywords: Insurance; Price
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Amin, Kaushik, Joshua D. Coval, and H. Nejat Seyhun. "Demand for Portfolio Insurance and Index Option Prices." Journal of Business 77, no. 4 (October 2004).
  • 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
Citation
Educators
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Coval, Joshua, and Erik Stafford. "Index Options." Harvard Business School Background Note 208-119, January 2008.
  • January–February 1976
  • Article

Option Pricing When Underlying Stock Returns are Discontinuous

By: Robert C. Merton
Keywords: Price; Stocks; Assets
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Merton, Robert C. "Option Pricing When Underlying Stock Returns are Discontinuous." Journal of Financial Economics 3 (January–February 1976): 125–144. (Chapter 9 in Continuous-Time Finance.)
  • January 2008
  • Background Note

Equity Options

By: Joshua Coval and Erik Stafford
The goal of this simulation is to understand the reliance of option values on volatility. When an investor trades an option, they are essentially trading volatility. Therefore, much of the focus in this lesson is on forecasting volatility. Students are able to use two... View Details
Keywords: Volatility; Forecasting and Prediction; Stock Options; Investment Return; Price; Market Transactions; Mathematical Methods; Value
Citation
Educators
Purchase
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Coval, Joshua, and Erik Stafford. "Equity Options." Harvard Business School Background Note 208-118, January 2008.
  • May 1976
  • Article

The Impact on Option Pricing of Specification Error in the Underlying Stock Price Returns

By: Robert C. Merton
Keywords: Price; Stocks
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Merton, Robert C. "The Impact on Option Pricing of Specification Error in the Underlying Stock Price Returns." Journal of Finance 31, no. 2 (May 1976): 333–350.
  • February 1993 (Revised December 1994)
  • Exercise

Corporate Financial Management: Options Exercises

By: Timothy A. Luehrman
This case presents four exercises designed to introduce students to applications of option pricing and decision-tree analysis to real corporate investment problems. Two of the four problems involve decision trees and two involve option pricing. Students should be... View Details
Keywords: Financial Management; Investment; Projects; Corporate Finance
Citation
Purchase
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Luehrman, Timothy A. "Corporate Financial Management: Options Exercises." Harvard Business School Exercise 293-095, February 1993. (Revised December 1994.)
  • March 2002 (Revised October 2002)
  • Case

Akamai's Underwater Options (A)

By: Brian J. Hall, Houston Lane and Jonathan Lim
Akamai's stock price declines dramatically with the NASDAQ in 2000, causing virtually all employee options to go underwater. Ownership and retention incentives are largely destroyed, and employee morale falls sharply. Management weighs the pros and cons of various... View Details
Keywords: Motivation and Incentives; Stock Options; Attitudes; Compensation and Benefits
Citation
Educators
Purchase
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Hall, Brian J., Houston Lane, and Jonathan Lim. "Akamai's Underwater Options (A)." Harvard Business School Case 902-069, March 2002. (Revised October 2002.)
  • June 2007 (Revised January 2009)
  • Case

Nextel Partners: Put Option

By: Timothy A. Luehrman and Douglas Scott
Nextel Partners' shareholders have voted to exercise a put option that will require the company's largest shareholder, Sprint Nextel Corp., to purchase all the shares it does not already own. However, the put option does not stipulate a price to be paid, but rather a... View Details
Keywords: Mergers and Acquisitions; Stock Options; Price; Public Ownership; Valuation
Citation
Educators
Purchase
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Luehrman, Timothy A., and Douglas Scott. "Nextel Partners: Put Option." Harvard Business School Case 207-128, June 2007. (Revised January 2009.)
  • 2016
  • Working Paper

Options-Pricing Formula with Disaster Risk

By: Robert J. Barro and Gordon Y. Liao
A new options-pricing formula applies to far-out-of-the money put options on the overall stock market when disaster risk is the dominant force, the size distribution of disasters follows a power law, and the economy has a representative agent with Epstein-Zin utility.... View Details
Keywords: Option Pricing; Rare Disaster; Price; Stock Options; Financial Crisis
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Barro, Robert J., and Gordon Y. Liao. "Options-Pricing Formula with Disaster Risk." NBER Working Paper Series, No. 21888, January 2016.
  • June 30, 2020
  • Article

Bipartisan Tax-Free Solution to Health Care Financing: Coupling HRAs With a Public Option

By: Regina E. Herzlinger, Richard Boxer and James Wallace
A combination of health insurance initiatives by the presumptive 2020 Democratic and Republican presidential nominees could expand health care coverage and significantly reduce costs, without raising taxes. Along the way, the combination could revitalize private... View Details
Keywords: Health Care Financing; Public Option; Health Reimbursement Arrangement (HRA); Health Care and Treatment; Insurance; Cost Management
Citation
Read Now
Related
Herzlinger, Regina E., Richard Boxer, and James Wallace. "Bipartisan Tax-Free Solution to Health Care Financing: Coupling HRAs With a Public Option." Health Affairs Blog (June 30, 2020).
  • April 2005 (Revised January 2006)
  • Background Note

Note on Basic Option Properties

Options are contracts that give the right, but not the obligation, to either buy or sell a specific underlying security for a specified price on or before a specific date. Explains the basis of options, covering fundamentals such as option terminology, the payoff... View Details
Keywords: Stock Options
Citation
Educators
Purchase
Related
Chacko, George C., Peter A. Hecht, Vincent Dessain, and Anders Sjoman. "Note on Basic Option Properties." Harvard Business School Background Note 205-105, April 2005. (Revised January 2006.)
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