You issued a non-callable bond paying 8% annual coupon but would like make it callable. How would you go about doing this using a swaption? Demonstrate with cash flows.

Buy Receiver swaption Benefits when rates go down as a call option You would enter a swap receiving fix 8 and paying a lower floater

7

agreed with long receiver swaption. What’s 7 bpdulog?

I have a different view from the above: The price of a callable bond does not increase proportionately when interest rates go down – so essentially we need to replicate the negative convexity. Therefore, the swaption has to result in a payout when interest rates decrease – that happens when you SHORT a swaption as a fixed rate payer/floating rate receiver Result: – when interest rates go down, non-callable increases in value, but your payoff from the swaption becomes negative - net result, increase in value of callable is offset by the swaption – when interest rates go up, non-callable decreases in value, with no effect on swaption it cannot be exercised (ie, as interest rates are greater than the strike rate). You’ve however have pocked the swaption premium – which marginally improves your net result. As in the case of a callable, when interest rates go up, the value of the call goes down and price of the callable goes marginally up. Let me know whether this analysis is correct.

stevenevans Wrote: ------------------------------------------------------- > > Let me know whether this analysis is correct. You are making it way too complicated. When you buy a receiver swaption, you have paid a premium for it. When interest rates go down, you would not want to pay the 8% on the coupon. So you exercise the swaption. Cash flows: Pay 8% on bond Receive 8% of fixed side of swap Pay LIBOR (which has gone down) NET: Pay LIBOR. When interest rates go up, you are quite happy that you only have to pay 8%. So you do not exercise the swaption. Cash flows: Pay 8% on bond.

That strategy seems right when you want to protect from the downside What we are trying to achieve is the negative convexity of a callable, which essentially means that you should not benefit from the upside when interest rates go down In your strategy, you’re payoff decreases when interest rates go down – so price goes up – which does not achieve the objective Let me think this through, perhaps I’m wrong but good question to ponder about

the question says, you issued the bond, therefore if you want to have positive convexity (as on short callable) you need to buy the option (receivers)

Got it, my apologies – I was looking at this from the investor perspective, not the issuer I’m stupid, really stupid!