Approximately pi proofs that the stock market can approximate pi

TL;DR

This paper presents three derivations of Polya's approximation for the expected range of a simple random walk, enabling estimation of financial volatility and pi from market data.

Contribution

It introduces new derivations of Polya's approximation, connecting random walk theory with practical financial volatility estimation.

Findings

Derived three new formulas for the expected range of a simple random walk.

Showed how to estimate pi from financial market high-low price data.

Demonstrated the application of these formulas to real-world financial data.

Abstract

We give three derivations of Polya's approximation for the expected range of a simple random walk in one dimension. This result allows for an estimation of the volatility of a financial instrument from the difference between the high and low prices, or, equivalently, for an estimation of pi from the ratio of the volatility to the difference between high and low prices.