Coupon Timing and Exercise of Embedded Bond Options
Summary
The document asks how coupon payments should be handled when valuing a callable or puttable bond on a binomial tree: should the coupon be added before applying the call or put exercise limit, or afterward? The answer emphasizes that the result depends on the specific bond terms. Calls commonly provide accrued interest, and some include an additional payment; puts generally cause the holder to forgo the next coupon, which helps explain why exercise often occurs just after a coupon date.
The discussion also notes that exercise may require advance notice and may be concentrated around coupon dates. Issuers can leave bonds outstanding even when a model suggests calling them, for business or refinancing reasons, and companies may seek to buy back debt through tenders. These contractual and behavioral details limit the precision of a simple tree model. The answer cautions that credit risk may also be handled only crudely, making scenario analysis and judgment important alongside quantitative estimates.
Key ideas
- Coupon treatment at exercise depends on the bond’s contractual terms.
- Callable bonds commonly compensate for accrued interest, and some include an extra payment.
- Put exercise often sacrifices the upcoming coupon, encouraging exercise just after coupon dates.
- Notice periods and issuer decisions can make actual exercise differ from a model’s prediction.
- Credit risk and contractual details limit the precision of simplified bond-option models.
Tags
Full text
# How to handle coupon payments when pricing a bond with an embedded option? # How to handle coupon payments when pricing a bond with an embedded option? I'm using a binomial tree to price a bond that has an embedded call or put option. On every node that has a coupon payment, do you include the coupon payment then max/min out the value, or do you max/min out the value then apply the coupon? My guess is that for a call option, the issuer will make sure the value to the lender doesn't go beyond the call price, so we include the coupon, THEN min it out. But for a put option, the lender will make sure the value doesn't go beyond the put price, so we exclude the coupon, max the price out, THEN apply the coupon. Is this correct? Effectively, that's sort of like saying: assuming a continuously exercisable option, try to exercise the option 1 sliver of time before getting the coupon, then try to exercise it again 1 sliver of time after getting the coupon. ## Answer by Brian B (score 4) https://quant.stackexchange.com/a/2165 You have to look at the terms and conditions on your individual bond. The way the specifications usually work is that a call will result in accrued interest being paid, effectively making up for the lost coupon. Sometimes there's even an extra penalty. A put will result in a loss of coupon in almost all cases, and so is almost always done just after a coupon payment. Exercise must usually be preceded by a 30 day notice period, and is usually only considered near coupon dates. In many cases, a bond that "should" be called is left outstanding, either to keep the markets sweet or to avoid the headache and expense of a new issuance. Also in many cases, a bond will be "tendered for" by a company wanting to remove it from the markets. For these reasons, quantitative modeling of bond options and their interest rate dependence is only of approximate use. Add that to the fact that credit modeling is often skipped, or is primitive when included, and you find that scenario considerations and human intuition play a bigger role in that market than many people expect.
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