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Essential Mathematical Concepts for Algorithmic Trading

QuantInsti

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Excerpt

Mathematical Concepts

Starting with the mathematical concepts of trading, it is a must to mention that mathematical concepts play an important role in algorithmic trading. Let us take a look at the broad categories of different concepts here:

  • Descriptive Statistics
  • Probability Theory
  • Linear Algebra
  • Linear Regression
  • Calculus

Measure of Central Tendency

Here, Mean, Median and Mode are the basic measures of central tendency. These are quite useful when it comes to taking out average value from a data set consisting of various values. Let us understand each measure one by one:

Mean

This one is the most used concept in the various fields concerning mathematics and in simple words, it is the average of the given dataset. Thus, if we take five numbers in a data set, say, 12, 13, 6, 7, 19, 21, the formula of the mean is

which makes it :

(12 + 13 + 6 + 7 + 19 + 21)/6 = 13

Furthermore, the trader tries to initiate the trade on the basis of the mean (moving average) or moving average crossover.

Here, let us understand two types of moving averages based on the ranges (number of days) of the time period they are calculated in and the moving average crossover:

  1. Faster moving average (Shorter time period) –

A faster moving average is the mean of a data set (stock prices) calculated over a short period of time, say past 20 days.

2. Slower moving average (Longer time period) –

A slower moving average is the one that is the mean of a data set (stock prices) calculated from a longer time period say 50 days.

Now, a faster-moving average and a slower moving average also come to a position together where a “crossover” occurs.

According to Wikipedia, “A crossover occurs when a faster-moving average (i.e., a shorter period moving average) crosses a slower moving average (i.e. a longer period moving average). In other words, this is when the shorter period moving average line crosses a longer period moving average line.”

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