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I know how to value a standard zero coupon bond but how would you value a zero coupon bond that is callable and you assume it will be called? With the formula:

Value = F / (1 + r)^t

Would the face value change or just the time to maturity change to the time until the call date?

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It would not make much sense (from issuer point of view) for the bond to be called at full face value. It would be a windfall for the investor.

There is usually a set schedule of Call Prices and if the ZCB is called in a particular year the redemption amount will be taken from a lookup in this table of values. This RV and the hypothesized call date is what you would use in your formula to value the bond. Often the table is constructed to produce predetermined yield(s) in the event of call.

Details differ depending on the issue

Some Examples

https://definedterm.com/zero_coupon_callable_bond

http://www.reuters.com/article/asia-bonds-idUSL4N0XY39W20150508

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  • $\begingroup$ A follow up question that I have is who issues these, who buys them and why? $\endgroup$
    – nbbo2
    Sep 12, 2016 at 15:43

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