The Marginal Revolution Podcast

Episode: "The Quest to Price Options"

Hosts: Alex Tabarrok (A), Tyler Cowen (B)
Date: December 17, 2024

Overview

This episode delves into the “quest” for a formula to price options – one of the landmark achievements in modern finance and economics. Alex Tabarrok and Tyler Cowen vividly trace the arc from options trading’s historical quirks to the breakthrough Black-Scholes formula, unpacking both the high mathematics involved and the human stories behind the discoveries. They also show how the legacy of options theory extends far beyond Wall Street, informing everything from unemployment to public policy.

Key Discussion Points & Insights

1. Understanding Options: Definitions and Intuition

• Definition of Options:
  • Call Option: Right to buy an asset at a certain price (strike price) before a set date.
  • Put Option: Right to sell an asset at a certain price before a set date.
  • Example: “I might have the right to buy a stock for a price of $10 anytime in the next three months. So in this example, $10 is the ... strike price, and three months is the time period.” (A, 00:36)
• Historical context: Options-like instruments date back centuries, but public markets for such instruments truly emerge in the US in the 1970s.
• The challenge: How should an option be fairly priced, especially when the value is unclear in the “middle” scenarios?

2. First Attempts and the Overlooked Genius of Louis Bachelier [04:00–09:53]

• Louis Bachelier (French mathematician, dissertation 1900):
  • First to apply mathematics to financial speculation, utilizing early ideas of randomness in price movements.
  • “He knows from his time at the Bourse that stock prices kind of look random ... the only thing that should move prices would be news. And news by definition is random. So he’s got Fama’s [efficient markets hypothesis] right there, right?” (A, 07:28)
• French tradition: Mathematicians inventing economic ideas solo, largely ignored due to advanced mathematics.
  • “It’s a French thing, not a British thing ... the French, my goodness, it's mathematical and just there it is, it arrives.” (B, 05:27)
• Bachelier’s work foreshadows Brownian motion and is later rediscovered by economists like Samuelson.
• Irony: Bachelier’s ideas were even referenced by Keynes, but the significance to option pricing wasn’t noticed.

3. Brownian Motion and the Role of Einstein [08:30–09:53]

• Einstein’s contribution: Provides mathematical explanation for Brownian motion (random movement of particles), crucial for random process modeling.
• Samuelson later argues Bachelier’s mathematics on the topic surpassed Einstein’s.
• Anecdote: A postcard from Leonard Savage (famed statistician) alerted Samuelson to Bachelier’s work, underlining the importance of academic “network effects.”

4. Paul Samuelson and the Next Wave of Progress [10:53–15:02]

• Samuelson: Not the undisputed “GOAT” but “the most influential economist of the 20th century” (A, 11:28).
• His 1965 paper attempts option pricing for “warrants:”
  • “He takes the first crack at the problem in 1965 ... and in it he credits Bachelier.” (A, 12:12)
  • Even for Samuelson, the mathematics was “tough stuff.”
• Hidden history: Multiple people such as Sheen Kasuf and Edward Thorp also investigate option pricing – sometimes with profit in mind.

5. Enter Black, Scholes & Merton – The Modern Solution [15:10–21:47]

• Robert Merton (Samuelson’s student) and the parallel work of Fisher Black & Myron Scholes are introduced.
• The capital asset pricing model (CAPM) and the concept of “risk as covariance” revolutionize finance, setting the stage for option pricing.
• Key Insight:
  • The real breakthrough is hedging: “if you had an option and then hedged your option position, the rate of return on that hedged position had to be the same as the rate of return on the safe asset. And that was the key condition...” (B, 19:41)
• Both CAPM and arbitrage approaches appear in early versions of the Black-Scholes paper.

6. Recognition, Publication, and the “Credit Problem” in Science [21:23–25:44]

• Merton’s role is under-credited even though he’s key to the arbitrage-based solution.
• “We tend to call it the Black-Scholes option pricing formula ... it should be Black, Scholes, Merton.” (A/B, 21:30)
• Merton delays his own paper to make sure Black and Scholes are published first – a rare gesture of academic generosity.

7. Adoption, Impact, and Hidden Histories [25:44–29:43]

• Initial skepticism: “Black and Scholes, they start shopping the paper around and actually it doesn’t receive a very good reception.” (A, 21:47)
• With the Chicago Board Options Exchange (CBOE) launched, the options market explodes.
• Real-world impact: Empirical data often nudges theory. “The market was implicitly including ... the possibility of a takeover” in option prices, which even the model missed. (A, 27:36)
• Hidden figures: Thorp (“the guy who beat the casinos”) and Kasuf made substantial money using their own models, even if never fully recognized by academia.

8. The Broad Application of Option Theory: From Insurance to Real Life [32:14–43:52]

a) Insurance as an Option

• “Take car insurance for example. You can think about that as a put option.” (A, 32:14)
• Policies like FDIC’s guarantees to banks are massive put options; option pricing helps governments estimate their real cost.

b) Unemployment, Business Cycles, and Investment Decisions

• “You would prefer to exercise that option by staying out of the labor pool and waiting for the better job to come along...” (B, 34:07)
• Classical price signals (Hayek/Mises) often don’t suffice; uncertainty and risk premiums (not just interest rates) drive real decisions.

c) Option Value in Policy and Everyday Life

• Policy moves that lower exit costs (easy firing, bankruptcy laws) make hiring and investment more responsive.
• Illustration: "In the United States, when you hire someone, it's like going on a date. In Europe, when you hire someone, it's like getting married." (A, 42:24)

9. Legacy and Continuing Influence

• “Options pricing theory... extends well beyond the trading floors, shaping areas like the creation of new financial tools, portfolio insurance, guiding investment decisions ... [and] has revolutionized the understanding of and the management of uncertainty and risk.” (A, 43:04)
• "As a concept it's still underrated." (B, 43:39)

Notable Quotes & Memorable Moments

• On the arbitrary advance of French mathematical economics:
  “It’s a French thing, not a British thing... the French, my goodness, it’s mathematical and just there it is, it arrives.” (B, 05:27)

• On the randomness underlying markets:
  “The only thing that should move prices would be news. And news, by definition, is random. So he’s got Fama’s [efficient markets hypothesis] right there, right?” (A, 07:28)

• On the true insight of Black and the transformative arbitrage idea:
  “He realized that if you had an option and then hedged your option position, the rate of return on that hedged position had to be the same as the rate of return on the safe asset. And that was the key condition...” (B, 19:41)

• On market wisdom exceeding academic models:
  “It turned out that the market was implicitly including in the price of these options the possibility of a takeover. OK, so the market sometimes knows even more than the model knows.” (A, 27:36)

• On the broad conceptual reach of options:
  “A lot of decisions that we have to make have an options-like aspect and thus can be understood with options pricing theory.” (A, 32:14)

• On options theory’s importance:
  “I would sum up by saying it's one of the most important ideas in economics. It came oddly late and as a concept it's still underrated.” (B, 43:39)

Timestamps for Key Segments

• [00:30–03:44] — Options explained; historical and intuitive background.
• [04:00–09:53] — Louis Bachelier, early mathematics, and random movements.
• [10:53–15:10] — Paul Samuelson’s role; the hidden early work of Kasuf and Thorp.
• [15:10–21:47] — Merton, Black, Scholes, and the mathematical breakthrough.
• [21:23–25:44] — Academic credit, publication hurdles, and the generosity of Merton.
• [25:44–29:43] — Adoption in markets, real-world tests, and the practical edge of early practitioners.
• [32:14–36:27] — Insurance, options in public policy, and unemployment as option value.
• [36:27–43:52] — Application to economic cycles, investment, exit costs, and the pervasiveness of option logic in decision-making.

Tone and Style

The conversation is lively, sharp, and laced with intellectual curiosity, often irreverent (“nerdy winsomeness”) but deeply respectful toward the science, the mathematicians, and the hidden contributors. Personal anecdotes (Tyler’s hiring interview with Kasuf, phone calls with Fisher Black) humanize the technical topic, while the hosts’ evident admiration for the subject gives the entire episode an energizing, almost celebratory tone.

Conclusion

Options pricing theory, born of randomness, arbitrage, and a little French mathematical moxie, is among the most powerful frameworks to emerge from 20th-century economics. It not only transformed finance, but it also provided vital insight into uncertainty, risk, and human decision-making across a world of applications. As the hosts sum up:
“I would say it’s one of the most important ideas in economics. It came oddly late and ... is still underrated.” (B, 43:39)