# Yield to call on American style callable bond

(Assuming current bond price is quoted and maturity, par value, strike price all known..)

I was wondering how do we calculate yield to call on American style callable bonds after the call date has passed - meaning - when the bond can be called any day until maturity.

What we use for maturity date to calculate the yield to call ?

Thanks!!

There is a field "call notice days" or something similar on Bloomberg and similar bond indicative data databases. If this field is not populated, then assume 30 days. The bond issuer must give at least this many calendar days' notice if they choose to exercise.

To find the yield to worst of an American or Bermudan callable bond, the common practice is to loop on all potential call dates from today + call days until maturity, calculate the yield if the call is exercised on this date, and find the worst yield possible.

Hence, likewise, the earliest possible American exercise date is today + call days, so you use that date to calculate yield to call. For a bermudan, use the next date that is >= today + call days. This is consistent with what Bloomberg terminal does.

The issuer can't announce a call sooner that call days.

P.S. Puttable bonds are common in Russia and India, but much less common in other markets. A yield-to-worst calculation for a bond that might be puttable and/or callable should assume that the bond issuer will look for the yield that's worst for the bond holder, but the bond holder will look for the yield that's worst for the bond issuer. You may want to think about the meaning of yield-to-call for puttable bonds.

• Good answer. Follow-up from my side: (1) isn't the method of "looping" over all possible dates computationally rather expensive? thinking of a perp w/ American call feature here... starting from today (+x days) and looping "until infinity" might take some time, even though it's a simple-to-value cashflow instrument. Is there some method like "bermudanizing" first, and then once the YTW is found, discretize this bucket finer again, etc.? (2) Do you know of some "reverse algorithm", i.e., given a bond's yield, can we backward engineer so to find the call date "priced by the market"? Aug 25, 2021 at 6:24
• thanks @KevinT ! 1 yes , very! Unfortunately, I don't know of any faster search in general than trying every date (quant.stackexchange.com/questions/51284 I too asked here), given that the call price (strike) and other features may vary over time. Try how long YTW of such bond takes on Bloomberg - sometimes many seconds, and they assume perp means ~2150. 2 sorry, same thing. Given yield and price, I'd try every date to find the fugit. Further, is the fugit's necessarily unique, or you just want the earliest one? Given yield only, is the price unique? Are such bonds quoted on yield? Aug 25, 2021 at 12:44
• Many thanks for the prompt and detailed replies to both. Really helpful. Sep 5, 2021 at 10:49