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Financial module >> Financial module > hurst

hurst

Compute the Hurst index on historical prices

SYNOPSIS

H=hurst(price [,period [,step]]);

Description

Given the historical prices of an asset the function computes the so-called Hurst index (or Hurst exponent) for fractional Brownian motion on the asset returns.

If the Hurst index H is 0.5, then the price process is a "regular" Brownian motion; if H>0.5, then the increments of the process are positively correlated; finally, if H<0.5, the increments of the process are negatively correlated.

The function also shows a scatter plot of the log of the sample length against the log of the variation coefficient of asset returns.

Parameters

price
column vector containing the historical prices of an asset (in general they are daily prices)
period
optional parameter: first set of prices used for estimating the Hurst index (by default it is 250 - i.e. the working days in a year)
step
optional parameter: increment in the set of prices used for estimating the Hurst index (by default it is 10). This is the increasing step in the rolling estimation.

Output

H
estimated Hurst index on the asset (log-) returns

Example

First we generate 1000 log-normally distributed daily prices for an asset whose initial values is 25 euros. First step is the creation of 1000 normal random variables (with mean 0.1/250 and standard deviation 0.2/sqrt(250))

-->M=grand(1000,1,'nor',0.1/250,0.2/sqrt(250));

Then we create the prices

-->S=exp(cumsum(M,1))*25;

Now we are ready to use the function. We use it on the first 100 prices and with a step of 10 days

-->H=hurst(S,100,10)

H = 0.5588872

We have a value close to 0.5 which means that the data should be more or less follow a Brownian motion.

Authors

Francesco Menoncin - Brescia University - 2010


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