Valuing a Callable Zero-Coupon Bond at Its Call Price

Summary

The document asks how to value a callable zero-coupon bond when assuming it will be redeemed on a call date. Its starting point is the standard present-value formula for a zero-coupon bond, and the answer clarifies that the maturity date alone is not the only input that changes. The relevant redemption amount is the scheduled call price for the assumed call date; that amount and the time remaining to that date are discounted to obtain a basic present value.

Call prices are commonly specified in the bond's terms, sometimes on a schedule designed to produce predetermined yields if the issuer calls. The answer cautions that redemption at full face value should not be presumed and that details depend on the issue. This is a simplified valuation conditional on a chosen call date. It does not model the issuer's incentive to call, uncertainty over whether or when a call occurs, interest-rate dynamics, or the option value embedded in the call feature. Those factors are needed for a fuller valuation when the call assumption is not simply imposed.

Key ideas

• A callable zero-coupon bond's assumed redemption value should come from its call-price schedule.\nThe call-date redemption amount and time to that date are the inputs to a basic discounted-value calculation.\nCall prices may be set to achieve specified yields upon redemption.\nTerms vary by issue, so the bond documentation determines the applicable redemption amount.\nA conditional present-value calculation does not capture uncertainty or the embedded call option.

Tags

# How to value a called zero coupon bond?


# How to value a called zero coupon bond?












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?

## Answer by nbbo2 (score 0, accepted)

https://quant.stackexchange.com/a/30107

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

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.