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Estimating Volatility from Daily OHLC Prices with the Method of Moments

Article arXiv papers · Author: Cristin Buescu et al.
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Summary

This document describes a method for estimating stock-price volatility from daily high, low, opening, and closing prices. It uses the expected range of an arithmetic Brownian motion and the method of moments. The opening price jump is treated as a consequence of unobserved price evolution during an after-hours trading period, incorporating overnight movement into the estimation framework. The resulting annualized volatility estimate is applied to Black-Scholes pricing for European options. The document also proposes a trading strategy that seeks to profit when model prices differ substantially from market prices. The supplied description gives no estimation formulas, empirical results, thresholds for identifying price discrepancies, or transaction-cost analysis. It therefore outlines a modeling and trading approach, but does not establish that the option pricing or proposed strategy performs reliably in practice.

Key ideas

  • Daily highs, lows, opens, and closes are used to estimate volatility by the method of moments.
  • The expected range of arithmetic Brownian motion provides the basis for the estimator.
  • The opening price jump represents unobserved after-hours price evolution.
  • Annualized volatility estimates are used to price European options with Black-Scholes.
  • A proposed strategy targets large differences between model prices and market prices.

Tags

VolatilityOptionsDerivatives pricingStatistics
Full text
# An application of the method of moments to volatility estimation using daily high, low, opening and closing prices


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









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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.