An application of the method of moments to volatility estimation using daily high, low, opening and closing prices

TL;DR

This paper introduces a method to estimate stock volatility using daily high, low, open, and close prices through the method of moments, and applies it to option pricing and trading strategies.

Contribution

It applies the method of moments to volatility estimation using daily price ranges, incorporating after-hours jumps, and demonstrates its use in option pricing and trading.

Findings

Effective volatility estimation from daily price data

Application to Black-Scholes option pricing

Profitable trading strategy based on price discrepancies

Abstract

We use the expectation of the range of an arithmetic Brownian motion and the method of moments on the daily high, low, opening and closing prices to estimate the volatility of the stock price. The daily price jump at the opening is considered to be the result of the unobserved evolution of an after-hours virtual trading day.The annualized volatility is used to calculate Black-Scholes prices for European options, and a trading strategy is devised to profit when these prices differ flagrantly from the market prices.