Overhedging a Callable Bond with a Bermudan Payer Swaption

Summary

The document outlines an approximate way to cover the cash flows of a fixed coupon Bermudan callable bond using a fixed rate bond and a Bermudan payer swaption. The proposed portfolio holds both instruments. If the callable bond remains outstanding, the swaption is left unexercised and the bond is intended to offset the callable bond’s fixed payments. If the issuer calls the bond, the swaption is exercised to produce variable-rate swap cash flows.

The argument is for an overhedge: the portfolio is claimed to cover the callable bond’s outcomes, but may cost more than the bond itself. The text says a dealer may account for that excess cost in pricing. It gives no construction details, valuation, market assumptions, or numerical evidence, and the hedge depends on cash flow terms and exercise alignment matching as described. It is therefore a conceptual payoff argument rather than a complete replication recipe.

Key ideas

• A fixed rate bond and Bermudan payer swaption are proposed as a portfolio to cover a callable bond.
• If the callable bond is not called, the swaption can expire unused while fixed cash flows offset.
• If the bond is called, exercising the swaption is intended to provide variable rate cash flows.
• The proposed hedge is an overhedge and may cost more than the callable bond.

Tags

# Replicating the price of a (Bermudan) callable bond using a Bermudan swaption and bond


# Replicating the price of a (Bermudan) callable bond using a Bermudan swaption and bond












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?

## Answer by Daneel Olivaw (score 1)

https://quant.stackexchange.com/a/60028

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.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.