Risk-free, in this context, only means free from default risk. It ensures your numeraire is never zero, and generally simplifies things.The standard Black-Scholes model doesn't assume that the US dollar (and hence US Government bonds) has a constant value, only that it has a constant US dollar value, which is pretty obvious.I would suggest that looking for a genuinely 'risk-free security', free from default risk and from market risk, is a lot like looking for the ether reference frame. However, it is interesting to consider that the printing money argument applies as much to a companies shares as it does to a currency. A company never (as far as I know) has to default on an obligation to pay its own shares, which means that these shares are something like a risk-free asset to the company. For this reason, it could be argued that companies should be measuring financial risks using their own stock as numeraire.
Last edited by spacemonkey
on January 21st, 2011, 11:00 pm, edited 1 time in total.