Carry has nothing to do with decay. ITM euro-ex puts can trade at a discount to intrinsic value, = carry. They can appear to maintain +theta or gaining IV as the time to expiration nears and the ITM euro-put converges to intrinsic value at expiration. The rate of convergence is = the carry on holding the long put strike. It may seem as though vols are increasing, but it's already trading at a discount. Vol-strips can decrease rapidly, but the convergence will still be evident. This isn't an issue with american-exercise.
Same-strike calls and puts decay at the same rate, arb[model] dependent[independent].
Same-strike calls and puts decay at the same rate, arb[model] dependent[independent].
