Main Content

Price zero-coupon instruments given yield

prices
zero-coupon instruments given a yield. `Price`

= zeroprice(`Yield`

,`Settle`

,`Maturity`

)`zeroprice`

calculates
the prices for a portfolio of general short and long-term zero-coupon
instruments given the yield of reference bonds. In other words, if
the zero-coupon computed with this yield is used to discount the reference
bond, the value of that reference bond is equal to its price.

adds
optional arguments for `Price`

= zeroprice(___,`Period`

,`Basis`

,`EndMonthRule`

)`Period`

, `Basis`

,
and `EndMonthRule`

.

To compute the price when `Period`

is `1`

or `0`

for
the quasi-coupon periods to redemption, `zeroprice`

uses
the formula

$$Price=\frac{RV}{1+\left(\frac{DSR}{E}\times \frac{Y}{M}\right)}$$

.

*Quasi-coupon periods* are the coupon periods
that would exist if the bond were paying interest at a rate other
than zero.

When there is more than one quasi-coupon period to the redemption
date, `zeroprice`

uses the formula

$$Price=\frac{RV}{{\left(1+\frac{Y}{M}\right)}^{Nq-1+\frac{DSC}{E}}}$$

.

The elements of the equations are defined as follows.

Variable | Definition |
---|---|

| Number of days from settlement date to next quasi-coupon date as if the security paid periodic interest. |

| Number of days from settlement date to the redemption date (call date, put date, and so on). |

| Number of days in quasi-coupon period. |

| Number of quasi-coupon periods per year (standard for the particular security involved). |

| Number of quasi-coupon periods between settlement date and redemption date. If this number contains a fractional part, raise it to the next whole number. |

| Dollar price per $100 par value. |

| Redemption value. |

| Annual yield (decimal) when held to redemption. |

[1] Mayle, Jan. *Standard Securities Calculation Methods.* 3rd
Edition, Vol. 1, Securities Industry Association, Inc., New York,
1993, ISBN 1-882936-01-9. Vol. 2, 1994, ISBN 1-882936-02-7.

`bndprice`

| `cdprice`

| `tbillprice`

| `zeroyield`