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Duration does not go down 1-for-1 with time.
Correct. Although it could, zero coupon bond.

...and stable interest rates.???

jrr.

We do agree, except on this I have a slight question.

If we are talking about straight "duration," then interest rates are irrelavent. The duration for a zero coupon bond is equal to the time to maturity. Duration is the weighted average of the times of the cash flow, there is nothing in the equation for interest rates. (no discount)

Now, if we are talking about a modified duration in some form, then I would be happy to get on the same page, this may be just a definition question, just let me know what you are calling duration.

And
Holding a Put option = option to sell
Holding a call option = option to buy

You own the variable-rate bond and the option, you're able to redeem part of it at par any time a maturity date comes up. You have no guarantees about what price you'd be able to buy more of it at.

The way I view this is that it is a call option; Here is why, when a bond matures, you do not have the right to decide if you want to redeem (sell) the bond - It is sold, you get the cash. What you do have is the embedded right to purchase (a call) the next bond. So, the cash flow gives the holder the right, but not the obligation to buy. If interest rates are up, then the call option due to maturity has paid off.

I can see looking at the bond par value as the floor, or minimum the same as would be provided by a put, but when maturity comes up, you do not have the right, but instead, you do have the obligation to sell as if you had sold a call. But, you do have the feeling of, you can always sell the bond for face value, the same as a put would give you, well in this instance - a European Put.

That is both sides of the coin, "European Put" on the old bond, Call option on the next in line bond.

DrTarr