value of putable bonds

At high yield levels, as interest rates further increase, the value of a putable bond most likey:

a) increases at a decreasing rate b) decreases at an increasing rate c) decreases at a decreasing rate

Why is this? I thought if interest rates increase, price goes down and puts become more valuable. The only reason I can think of it is because the put is already in-the-money but that would not change the value anyways.

Holy crap… I have no clue. My guess would have been A. Would love to hear someone’s explanation for this.

Draw a price vs. yield curve, and remember that the price of a puttable bond is bounded below by the put price: nobody would sell a bond on the open market for $950 when they can get $960 by exercising their put option. The curve flattens out as you go to the right: the price decreases, but more and more slowly as yields increase.

My first guess was A as well. I actually figured out this question 5 minutes I posted it. Look at volume 5 page 568 as S2000 said. It shows the yield curve of the putable bond vs an option-free bond. Notice that at higher interest rates, the curve of the putable bond is above the option-free bond. The value of the putable bond is still decreasing at a decreasing rate.

Note: the question asks for the value of the the putable bond , not the value of the put option. As interest rates increase, the bond decreases in value but is offset a little bit by the put option. The different definitions was what confused me too.

This is my explanation. Correct me if it doesn’t make sense.

S2000magician so at low yields level, if market interest rates go up, price of a putable bond decreases at an increasing rate. is it right ?

I think still at decreasing rate… the change in next price (when yield increases) is smaller than option free bond.

that’s just my opinion…

edited :slight_smile:

No. The price of a putable bond decreases at a decreasing rate when interest rates increase no matter what the level of interest rates (yields). They have positive convexity everywhere.

Callable bonds, however, have negative convexity at low interest rates, so in that region the price decreases at an increasing rate when interest rates (yields) rise.