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OHLC data are one of the most popular kind of data available. Are there models which could incorporate all the information provided by OHLC - regular 1-minute frequency data for example ? Usually only close price is used, but high - low difference provides information about price volatility in given period - because width of range in population is correlated with variance in population (but dependence varies with population size, dependence is stronger for smaller sizes), if high-min is correlated with volatility we could use it in case of estimation of stochastic volatility model for example. Simple simulation of variance and max-min difference in case of population sizes - 10 and 20 :

n_iter=1e5
n_obs=10

out <- matrix(0, n_iter, 2)
out <- as.data.frame(out)
names(out)=c("var", "max - min")

for(i in 1:n_iter){

    x <- rnorm(n_obs)

    out[i,1] = var(x)
    out[i,2] = diff(range(x))

}

plot(out, main = paste("n_iter = ",n_iter,", n_obs = ",n_obs))
abline(lm(out[,2]~out[,1]), col = 2, lwd = 2)
cor(out)

# case population size 20
n_iter=1e5
n_obs=20

out <- matrix(0, n_iter, 2)
out <- as.data.frame(out)
names(out)=c("var", "max - min")

for(i in 1:n_iter){

    x <- rnorm(n_obs)

    out[i,1] = var(x)
    out[i,2] = diff(range(x))

}

plot(out, main = paste("n_iter = ",n_iter,", n_obs = ",n_obs))
abline(lm(out[,2]~out[,1]), col = 2, lwd = 2)
cor(out)
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    $\begingroup$ I'm sure you're already aware of Parkinson Volatility estimation method using HLC rather than just C. It's nice because far fewer observations are required. However it requires making a lot of assumptions about the asset's behaviour during the period (that it's Normal). Consider high frequency observations of eg futures prices and there is a lot of high/low ticking that deliberately extends the range without really providing new information. $\endgroup$ – GodLovesATrier Aug 5 '16 at 22:12
  • $\begingroup$ @GodLovesATrier "observations of eg futures" - does simply "eg" means "e.g." here ? $\endgroup$ – Qbik Aug 7 '16 at 10:45
  • $\begingroup$ Yes eg should be e.g. (for example) $\endgroup$ – GodLovesATrier Aug 7 '16 at 10:55
  • $\begingroup$ @GodLovesATrier yes, there are much more spikes in futures prices then in the underlying assets, do know how can I start study this phenomenon ? what are main causes and could we create arbitrage strategu based on it ? $\endgroup$ – Qbik Aug 7 '16 at 11:17
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Not a model as such, but this paper might be interesting to you:

A Simple Way to Estimate Bid-Ask Spreads from Daily High and Low Prices

It estimates bid-ask spreads from daily OLHC data. Perhaps you could use the same logic with minute data?

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If it is volatility you are interested in, a relevant paper is "Drift‐Independent Volatility Estimation Based on High, Low, Open, and Close Prices" by Dennis Yang and Qiang Zhang, The Journal of Business, Vol. 73, No. 3 (July 2000), pp. 477-492. This builds on the earlier HLC volatility estimator by Parkinson (1980) that was mentioned above.

Another application of OHLC data is to detect if prices crossed a certain level K during an interval of time (although it will not tell you at what time within the interval the level was crossed).

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