Callable and Puttable Bond Curve Questions

CFA Level II Fixed Income
#1

Hi,

I’ve a question about the price v.s. yield curve of callable and puttable bonds. The callable bond will show a negative convexity at lower yield and its price will be lower than the straight bond, and the puttable bond will show a more positive convexity at higher yield and its price will be higher than the straight bond.

Also the straight bond price will go to zero as yield approaches infinity. I dont understand why the puttable bond will approach its put price instead of zero as the yield approaches infinity. I think all the cash flow, no matter its the strike price or original cash flow will be discounted towards zero. Could anyone explain this to me?

#2

If the bond is putable at, say, par, why would you sell it on the open market at, say, $990 when you could put it back to the issuer for $1,000?

#3

I understand this logic if I dont consider the calculation part. I get confused when using the binominal tree method to think about this, if the r is very big, then I would expect to get a zero price due to the discount back to time 0.

Say at time 1, due to higher r, the discounted cash flow is very small $1, and my put price is $1,000. Then I will put, and discount the $1,000 back to time 0, it should be closer and closer to 0 as r moves up?

#4

When you discount the payment of $1,000 (plus the coupon) at time 1, you don’t use the time 1 discount rate; you use the time zero discount rate.