# how do traders typically hedge a callable zero coupon bond?

i've seen termsheets of callable accreting notional swaps where the accretion rate equals the fixed coupon rate. apparently these are used to hedge callable zcb's. but it doesnt seem to make sense! the fixed leg of the swap is paying coupons, whereas the zcb doesnt pay coupons. i guess maybe it is done like that to reduce credit risk. and then the question is , should the funding leg of the swap also have accreting notional? that seems a bit strange too.

Also, i am trying to think if the callable swap should have a call fee on it or not (and if so, what exactly), as for the callable zcb , there must be a call fee equal to the accrued notional (that is the equivalent of par for a zcb).

• I just wonder if the call price of the ZCB is fixed (par or some other predetermined price) or the call strike is expressed as yield or it may be a make-whole call (price will depend on interest rates)? Jan 25, 2021 at 17:57
• for a normal callable bond, if the issuer wants to call it, they pay par (100), and the bond is cancelled. the idea is , if the bond yield has gone down since issuance, then the issuer would call it, and then reissue debt at the lower market yield. for a callable ZCB, i assume its the same idea, ie the issuer would call it if they could re-issue the debt at a lower yield Jan 25, 2021 at 18:15
• This is the most common, but you should check before assuming. For example, this 1989 paper doi.org/10.2307/2330750 looked at 132 callable corporate ZCBs, 128 were callable at par, but in the other 4 "the call price was a function ofthe "accreted value." The accreted value is the present value of the face value ofthe bond discounted at the original yield to maturity Jan 25, 2021 at 18:23
• how are they defining 'par' for a ZCB? The yield on a zcb is the IRR , which is simply the rate at which it's current market price would accumulate to the final notional payout. if that yield is higher than the rate at which the firm could borrow currently in the market, then it makes sense for the firm to cancel the zcb, and reborrow at the market rate). Jan 25, 2021 at 20:25
• It would be better to just look at the bond's prospectus (RTFM:) than to guess. I'm just pointing out that the call can have >1 variants in practice, which would affect how you'd hedge the bond. Jan 25, 2021 at 20:54