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I have heard that the price of a (Bermudan) callable bond can be replicated (at least approximately) by a Bermudan swaption and ordinary bond (assume the callable bond pays a fixed coupon).

I was wondering if it is possible, how can one construct the Berm swaption, bond, and also combine them?

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  • $\begingroup$ My own thoughts: I know the Berm. swaption is meant to capture the optionality, but entering (or exiting) a swap introduces cash flows (like a floating leg) that a callable bond does not produce. Including a vanilla bond in the replication along with the Berm swaption does not seem to help with this issue. $\endgroup$ – d_797 Dec 16 '20 at 22:28
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I think the strategy is meant to be an overhedge. Consider a portfolio $\Pi$ consisting on long positions on both a fixed-rate bond $B$ and a Bermudan payer $V$. Then on all scenarios the payoff of $\Pi$ is at least equal to that of the callable bond $C$:

  • If $C$ is not called, then the swaption $V$ can be relinquished and the fixed cash flows from $B$ and $C$ offset each other.
  • If $C$ is called, then we exercise the swaption $V$ and receive a net variable cash flow of LIBOR plus spread from the swap.

Hence $\Pi$ must be more expensive than $C$. When trading this kind of bond a dealer might charge a fee to compensate for the overhedge cost.

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  • $\begingroup$ Thanks, would you happen to know how one would set up the Bermudan payer swaption? How is the spread obtained? $\endgroup$ – d_797 Dec 17 '20 at 2:51

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