The Trillion Dollar Equation
Veritasium
31 min, 22 sec
A single equation has revolutionized risk management and spawned trillion-dollar industries by allowing accurate pricing and hedging of financial instruments.
Summary
- The equation emerged from physics and was instrumental in creating a fair and efficient system for pricing options.
- Jim Simons, a mathematician, founded the Medallion Investment Fund, achieving unprecedented returns by using mathematical models to identify market patterns.
- The Black-Scholes-Merton equation provided a formula for fair option pricing, leading to a rapid adoption by the finance industry and the explosion of derivative markets.
- Derivatives markets, now valued in the hundreds of trillions, have the potential to stabilize the economy during normal times and exacerbate crashes during market stress.
- The success of mathematicians and physicists in finance challenges the Efficient Market Hypothesis, suggesting that markets can be beaten with the right models and resources.
Chapter 1

The size and utility of derivative markets are vastly unknown to the public, despite being developed from a single equation derived from physics.
- This equation is the foundation for four multi-trillion dollar industries and has transformed risk approaches.
- Physics concepts like heat transfer and atom discovery influenced financial strategies used by mathematicians and scientists.
- Jim Simons set up the Medallion Investment Fund in 1988, which outperformed market averages for 30 years.
- Despite Jim Simons' success, being proficient in mathematics does not guarantee financial market success, as demonstrated by Isaac Newton's losses.
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Chapter 2
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Louis Bachelier and others pioneered the use of mathematics to model financial markets and the pricing of complex contracts like options.
- Louis Bachelier, whose parents died when he was 18, moved to Paris to study physics and worked at the Paris Stock Exchange, sparking his interest in options.
- Thales of Miletus executed the first known call option by securing the right to rent olive presses in anticipation of a bumper crop of olives.
- Options offer the right to buy (call option) or sell (put option) an asset at a later date for a specified price, which can limit downside risk, provide leverage, or serve as a hedge.
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Chapter 3
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The Black-Scholes-Merton equation, derived from mathematical models, revolutionized financial markets by accurately pricing options and derivatives.
- The equation provided a fair pricing mechanism for both option buyers and sellers, balancing the expected returns for both parties.
- The Chicago Board Options Exchange, founded in the same year the equation was published, led to rapid and widespread adoption in the finance industry.
- The equation enabled the creation of new markets, the growth of derivative markets, and provided tools for hedging and leveraging investments.
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