Hedging Callable Bonds with Bermudan Receiver Swaptions

# Callable Bond and Bermudan Swaption similarity


# Callable Bond and Bermudan Swaption similarity












If I have issued a callable bond , I will call the same when the yield goes below the strike and similarly (not same), I will enter into a receiver swap when the swap rate goes below the strike.

Is it fair to say Short callable bond and receiver Bermudan Swaption has similar risk nature (assuming call dates match with Swaption schedule) and can be used as hedges for one another? I am sure we need some form of convexity adjustment though as one is an option on yield and the other one is an option on swap rate ? Even if we assume the bond to be completely credit risk free , there has to be adjustment to match the yield and swap rate ?

## Answer by dm63 (score 3)

https://quant.stackexchange.com/a/83821

Yes, the issuer of a callable bond often sells a Bermudian receiver swaption to hedge the long call option in the bond. You are correct in saying that in fact one is an option on bond yields and the other is an option on swap rates, so they are not exactly the same thing.

Several scenarios can occur: if the bond yield and swap rate move closely together (say at a constant spread), then the options are exercised at the same time. If the swap rate moves down but the bond yield does not, then the swaption may be exercised and the bond issuer may decide to enter into a new swaption instead of calling the bond. Finally if the bond yield goes down but the swap rate does not, the issuer might call the bond but will then need to buy back the unused swaption.

Note that this is not a convexity adjustment , it is just that the options are on different underlying which can sometimes create asymmetrical outcomes. To be fair this is quite rare since most of the time bonds and swaps move roughly together.

## Answer by Dimitri Vulis (score 0)

https://quant.stackexchange.com/a/83822

It depends.

Callable bonds discussed in popular textbooks focus on but one scenario: investment grade issue sells fixed-coupon bonds when risk-free interest rates are relatively high, calls the bond when/if interest rates decrease, causing bond yield to decrease. For example, U.S. Treasury used to issue callable bonds when US yields were about 15% in the 1970s. In this case the underlying is indeed an interest rate instrument, although the option style needn't be Bermudan.

Many issuers (and buyers) of fixed-coupon bonds hedge their interest rate delta, often with (static) interest rates swaps. Some issuers (and buyers) of callable (and in some markets putable) bonds hedge their interest rate vega with interest rate swaptions. The vega hedges sometimes have to be dynamically readjusted.

But if instead you run SRCH on Bloomberg terminal to sample random callable bonds, you'll see many other use cases for callables. I'll leave it at exercise to see which ones are more common and guess the issuers' motives.

For example, a high yield issuer sells a bond, hoping that later the issuer's credit spread tightens, driving down the bond's yield.

Or, instead of the strike expressed as fixed clean price, many bonds come with a "make whole" call - the strike is not fixed, but is calculated by discounting the bond's remaining cash flows with a risk-free benchmark, such as treasury, plus some fixed spread.

Or, the bond has a call 1 year before maturity, which can be expected to be exercised not because it might be in the money, but because having outstanding debt with <1 year to maturity creates inconveniences for some issuers.

Or, an issuer sells a 10 year bond callable in 2 years, very far in the money - making it look like long term debt on accounting statements, but taking advantage of 2 year yields being lower than 10 year yields.

There are others.