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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.

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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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