Isn’t a zero-coupon perpetual bond not worthless if the relevant government has some probability of buying them back? A government issues perpetual bonds with no interest payments, no coupons: Most economists that are not hyper-dovish would argue such a bond is intrinsically worthless. However, if a government were desperate for some form of credit in regard to these instruments, wouldn’t there be some probability of the government buying these instruments back and thus granting them value?
If I understand you correctly, the bond pays out nothing whatsoever. Such a bond must be worthless. The value of the bond is equal to the net present value, i.e. the sum of the discounted value of all future cash flows, which are zero in your case. If the government would buy it back, it would necessarily buy it back at a price of zero. Therefore, the bond will remain worthless in any case.