If your branch (old one) once again merged back to master doesn't give expected result.I have using python script to find initial branch commit Id. 
git rev-list --first-parent changeset
--first-parent follow only the first parent commit upon seeing a merge commit.
Iterate changeset's  from above command until parent branch found.
def status_check(exec_command, exec_dir=None, background=False):
    if exec_dir:
        os.chdir(exec_dir)
    res = subprocess.Popen(exec_command, shell=True, stdout=subprocess.PIPE, stderr=subprocess.PIPE)
    if not background:
        result = res.communicate()
    return result
def findNewBranchCommits(changeset=None):
    cmd = "git rev-list --first-parent "+ changeset
    rev_list = status_check(cmd,self.module_dir)
    rev_list = str(rev_list[0]).split('\n')
    rev_list = list(filter(None, rev_list))
    for x in rev_list:                      # Iterate until branch base point
        rev_cmd = "git branch --contains " + x
        rev_cmd = status_check(rev_cmd,self.module_dir)
        rev_cmd = str(rev_cmd[0]).split('\n')
        if(len(rev_cmd) > 2): 
            print "First Commit in xxx branch",x
            break
findNewBranchCommits(changeset)