Question

Why do we need to predict stock market prices?

Answer 1

A martingale is a mathematical series in which the best prediction for the next number is the current number. The concept is used in probability theory, to estimate the results of random motion. For example, suppose that you have $50 and bet it all on a coin toss. How much money will you have after the toss? You may have $100 or you may have $0 after the toss, but statistically, the best prediction is $50 -- your original starting position. The prediction of your fortunes after the toss is a martingale. (To learn how this applies to trading, see Forex Trading the Martingale Way.)

In stock option pricing, stock market returns could be assumed to be martingales. According to this theory, the valuation of the option does not depend on the past pricing trend, or on any estimate of future price trends. The current price and the estimated volatility are the only stock-specific inputs.

A martingale in which the next number is more likely to be higher is known as a sub-martingale. In popular literature, this motion is known as a random walk with upward drift. This description is consistent with the more than 80 years of stock market pricing history. Despite many short-term reversals, the overall trend has been consistently higher. (To learn more about random walk, read Financial Concepts: Random Walk.)

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