FLASH FRIDAY: 50 Years of the Equation that Built Wall Street
- Thread starter ETJ
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There is some merit to BS. It focused on the variables that are important to consider. However, only a Fool would actually use it.
Ian Stewart, emeritus professor of mathematics at the University of Warwick included the Black-Scholes formula in his book Seventeen Equations That Changed the World, calling it the “Midas Formula.” He asked: “How did the biggest financial train wreck in human history come about? Arguably, one contributor was a mathematical equation.”
Stewart explained that the equation expresses the rate of change of the price of the derivative, with respect to time, as a linear combination of the price of the derivative itself, how fast that changes relative to the underlying asset price and how that change accelerates. However, it assumes perfect information, perfect rationality, market equilibrium and the law of supply and demand.
“If the assumptions behind the model ceased to hold, it was no longer wise to use it,” wrote Stewart. “But as time passed and confidence grew, many bankers and traders forgot that; they used the equation as a kind of talisman, a bit of mathematical magic that protected them against criticism.”
Here are some interesting exercises.
1. How does the time value of the option change with respect to time. Is it a linear function? As an example - if you held an option over the weekend, how would any formula predict what the price of the option would be on the open - Monday? Is the decrease in time value a continuous function?
2. How is the volatility determined and what causes it to change over the course of trading hours. Is this a linear function?
At the heart of any theoretical model is ceteris paribus and this never holds.
However, it assumes perfect information, perfect rationality, market equilibrium and the law of supply and demand.
Ian Stewart, emeritus professor of mathematics at the University of Warwick included the Black-Scholes formula in his book Seventeen Equations That Changed the World, calling it the “Midas Formula.” He asked: “How did the biggest financial train wreck in human history come about? Arguably, one contributor was a mathematical equation.”
Stewart explained that the equation expresses the rate of change of the price of the derivative, with respect to time, as a linear combination of the price of the derivative itself, how fast that changes relative to the underlying asset price and how that change accelerates. However, it assumes perfect information, perfect rationality, market equilibrium and the law of supply and demand.
“If the assumptions behind the model ceased to hold, it was no longer wise to use it,” wrote Stewart. “But as time passed and confidence grew, many bankers and traders forgot that; they used the equation as a kind of talisman, a bit of mathematical magic that protected them against criticism.”
Here are some interesting exercises.
1. How does the time value of the option change with respect to time. Is it a linear function? As an example - if you held an option over the weekend, how would any formula predict what the price of the option would be on the open - Monday? Is the decrease in time value a continuous function?
2. How is the volatility determined and what causes it to change over the course of trading hours. Is this a linear function?
At the heart of any theoretical model is ceteris paribus and this never holds.
However, it assumes perfect information, perfect rationality, market equilibrium and the law of supply and demand.
BS was 1973 - think about computing power. Most laptops took too long to calculate cox - ross to trade. Today's computing power has allowed hundreds of new pricing techniques to flourish. The book discusses much of that. BS was the pioneering work and the foundation of what we do today. There are even warrant models that predate BS by a generation.
There are dozens of situations BS doesn't do well, but that doesn't change the fire it lit 50 years ago.
Today I can do a Monte Carlo simulation on my phone.
There are dozens of situations BS doesn't do well, but that doesn't change the fire it lit 50 years ago.
Today I can do a Monte Carlo simulation on my phone.
Hmm. what alternative to BSM is there?
I'm not aware of any real alternatives, so let me know.
Which model is it?