# Model which fully incorporate OHLC data (higl ald low also)

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)

• 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. – GodLovesATrier Aug 5 '16 at 22:12
• @GodLovesATrier "observations of eg futures" - does simply "eg" means "e.g." here ? – Qbik Aug 7 '16 at 10:45
• Yes eg should be e.g. (for example) – GodLovesATrier Aug 7 '16 at 10:55
• @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 ? – Qbik Aug 7 '16 at 11:17