# Callable and Puttable Bond Curve Questions

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?

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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?

Simplify the complicated side; don't complify the simplicated side.

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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?

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.

Simplify the complicated side; don't complify the simplicated side.

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