A long callable bond can be replicated using a long option-free bond plus a short receiver swaption.

WHY is the above true?

The long callable bond has a call option that is short for the investor and long for the issuer.

A long option-free bond is the identical bond above with the exception of the call option. So you basically want to add something that will replicate the call option’s features. The receiver swaption has the same interest rate relationship to that call option above. If interest rates go down, the call option will be exercised by the bond issuer. The receiver swapton will also be exercised by the buyer because if rates go down, he will keep the fixed rate and pay a lower libor.

So you short the call option to replicate the callable bond.

Now to get a better understand, how would you replicate a puttable bond… using a option-free bond and what type of swaption?

you would LONG a payer swaption?

(do I still got it 125mph?!?)

You are cheating because you’re using level 3 material…