Is Stock Option Administration typically a function of Human Resources or Finance?

Our HR department is taking the position that our Company's stock option environment has become too complex. It used to be fairly straight forward, they were generally all non-qualified stock options that were exercised in a cashless sale. But now we also have Restricted Stock Units, net settlement exercises, exercised shares being purchased by the company in the form of treasury stock, etc. So the HR department is taking the position that the stock option administration should be done by the Finance department, which of course we disagree with. Our company is not large enough to hire a full-time person to do this function in a stand-alone department. My experience is that the stock option administration function is almost always handled by HR. What is your experience on what department handles stock option administration?