Technical Analysis of the Currency Market: Classic Techniques for Profiting from Market Swings and Trader Sentiment

CHAPTER 7

Fibs Don't Fib

Leonardo of Pisa, who lived from 1170 to 1250 and is better known as Fibonacci, is the most popular mathematician in trading, more famous even than Fischer Black and Myron Scholes, who invented the Black-Scholes formula, which is the foundation for all modern pricing of options. Fibonacci's contribution was far less complex than the Black-Scholes option pricing model. He is best known to traders for discovering the sequence of numbers that carries his name. The sequence proceeds like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, and so on. The series is constructed by choosing the first two numbers, known as the seeds, and then constructing the next number from the sum of the two prior numbers. The Fibonacci sequence obeys the formula P(n) = P(n − 1) + P(n − 2) and is an example of many such sequences in mathematics known as recursion relations.

The Fibonacci sequence has several neat mathematical properties, including:

1. If you take any three adjacent numbers, then square the middle number and multiply the two outside numbers, the difference between those two values will always be 1.
2. If you take any four adjacent numbers, then multiply the two outside numbers and multiply the two inside numbers, the product of the two outside numbers will always be 1 more or 1 less than the product of the inside numbers.
3. Finally, the sum of any 10 adjacent numbers will always be equal to the value of multiplying the seventh number of that ...