You can enter anything you want, but the true interest rate is the one that is already in the pricing.
That has to match the spot interest rate published outside the options model. ( Or it's expected future values ) .
This would work only for European options. For American options (like IWM) the method substantially changes the results of calculations.
No, I am expressing my own view about interest rate. So I cannot use or "trust" the implied interest rate... So these are two different things...
I suspect they don't match instantaneously... esp. on rate cut day. That's why I want to do some experiment, but first of all, where can I get a most-updated interest rate? And what exogenous interest rate shall I use?
Any website that publishes the interest rate would have some delay in updating it. Especially if you need to use Libor rate which I believe is the case. Since Libor rate I think is not even announced by any body. So what is your definition of 'instanteneous'? Those rates have to be updated on the web once a day at the closing. Unless of course you want to use real-time data by reuters. But this is unnecessary for most purposes.
You get implied volatility from the market price of options. The interest rate used is always the risk free rate which is usually 1 month LIBOR
I think you are right, and it should do that, as the american put can be higher in price than the american put in the absence of dividend and other unsual conditions. This would mean that the interest rate can be undervalued using the call-put calculation. I however have noticed that the ATM IWM put options are generally valued the same as a european put.
Your have the right to express whatever you want to express. For that you do not need a table. You need just your views. Remember, the market also express its view. It never fails in its views.