Compute expected maximum drawdown for Brownian motion
EDD = emaxdrawdown(Mu, Sigma, T)
Scalar. Drift term of a Brownian motion with drift.
Scalar. Diffusion term of a Brownian motion with drift.
A time period of interest or a vector of times.
EDD = emaxdrawdown(Mu, Sigma, T) computes
the expected maximum drawdown for a Brownian motion for each time
T using the following equation:
If the Brownian motion is geometric with the stochastic differential equation
then use Ito's lemma with X(t) = log(S(t)) such that
converts it to the form used here.
The output argument
ExpDrawdown is computed
using an interpolation method. Values are accurate to a fraction of
a basis point. Maximum drawdown is nonnegative since it is the change
from a peak to a trough.
To compare the actual results from
Malik Magdon-Ismail, Amir F. Atiya, Amrit Pratap, and Yaser S. Abu-Mostafa, "On the Maximum Drawdown of a Brownian Motion," Journal of Applied Probability, Volume 41, Number 1, March 2004, pp. 147–161.