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Notes
- 1.
Bachelier's random-walk model predicted that the spread in stock prices would increase as the square root of the time. But there was no limit in his model as to how low a stock could go. It could become negative, which means the company would be paying you to buy the stock. This flaw in Bachelier was first noted by the economist Paul Samuelson.
- 2.
A special case is a one-dimensional random walk. After each step the drunkard is equally likely to go forward or backward. Nonetheless he will move inexorably away from the lamp post. This example makes it clear why it takes longer to reach a certain average distance than it would if one just walked there.
- 3.
To be precise we are talking about the root mean square distance. This is the square root of the average of the square of the distance.
- 4.
This is reflected in the conditions under which the equation is solved. What is specified is the future value of the option at the time it is exercised. This is either zero or the strike price less the amount you have borrowed depending on how the stock's price has evolved. When you solve a physics equation you generally use data from the present to find your solution, which then allows you to predict the future.
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(2008). Black-Scholes. In: Physicists on Wall Street and Other Essays on Science and Society. Springer, New York, NY. https://doi.org/10.1007/978-0-387-76506-8_2
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