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Estimating OHLC Prices from Bid, Ask, and Close Data

Article Quant Q&A · Author: pyCthon
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Summary

The document asks whether open, high, and low prices can be reconstructed when a data source records only bids, asks, and closes. The answer says exact recovery is not possible from those observations alone. In particular, opens and closes are typically defined by the first and last trades, so bid or ask quotes do not determine the open.

For rough estimates, it suggests using the midpoint of bid and ask for the open, the highest observed bid for the high, and the lowest observed offer for the low. These are approximations rather than recovered trade prices: quote extrema may differ from actual transaction extrema, and the data may omit the first trade. The document gives no empirical comparison or validation of the estimates, so their accuracy depends on the market and sampling conventions.

Key ideas

  • Exact OHLC reconstruction is not possible from bid, ask, and close observations alone.
  • The open usually reflects the first traded price, which quotes do not identify.
  • A bid-ask average can serve as a rough open estimate.
  • The highest bid and lowest offer can approximate the high and low, respectively.

Tags

Market microstructureStatistics
Full text
# Estimate Open, High and Low prices from bid, ask and close prices


# Estimate Open, High and Low prices from bid, ask and close prices












I know it's possible to efficiently estimate bid/ask spreads from OHLC prices and there are several methods to do so. However I have a data source that contains only bids, asks and close prices, no High, Low or Open prices. Is it possible to do the inverse, estimate the Open, High and Low prices from bids, asks and close prices?

## Answer by Hans-Peter Schrei (score 2)

https://quant.stackexchange.com/a/75045

To my knowledge it is not possible to precisely recover the prices. Specifically in your setup, it is not possible to do this for the Open; as recording systems usually measure the Open and the Close as the first, respectively the last traded price, no matter the bid or the ask.

As for approximate estimates, it seems sensible to take an average for the Open and to take the highest bid as the High and the lowest offer as the Low.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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