Derivatives equivalencies

CFA Level II Derivatives
#1

Hi to everybody,

I have hard time understanding the logic behind this equivalencie:

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

Being long a callable bond means that you are long the bond and short the call with a discount on the bond equivalent to the premium we would get writing the call.

Being shot receiver swaption means that you are obligated to be the counterparty of the receiver swaption who profits from a decrease in interest rate and will exercice his option when the rate falls below the exercice price.

It means that being short receiver swaption gains when interest rise. If i am long a callable bond and interest rise the call won’t be exercice and I remain with a discount bond.

But and if me reasoning till there is correct i do not see the exact equivalencie.

Thanks.

#2

You are looking at the opposite sides of the two instruments and wonder why they don’t seem equivalent. Yes, when interest rate rise short receiver swaption gains, but this is exactly because the swaption won’t be exercised and you gain the premium, same with the short call (which won’t be exercised either). If interest rates fall, then both the swaption and short call will be exercised.

#3

Thank you Nenorr.