Fixed-Income Toolbox™

zeroprice - Price zero-coupon instruments given yield

Syntax

Price = zeroprice(Yield, Settle, Maturity, Period, Basis, 
EndMonthRule)

Arguments

`Yield`	Scalar or vector containing yield to maturity of instruments.
`Settle`	Settlement date. A vector of serial date numbers or date strings. `Settle` must be earlier than or equal to `Maturity`.
`Maturity`	Maturity date. A vector of serial date numbers or date strings.
`Period`	(Optional) Scalar or vector specifying number of quasi-coupons per year. Default = 2.
`Basis`	(Optional) Day-count basis of the bond. A vector of integers. 0 = actual/actual (default) 1 = 30/360 (SIA) 2 = actual/360 3 = actual/365 4 = 30/360 (PSA) 5 = 30/360 (ISDA) 6 = 30/360 (European) 7 = actual/365 (Japanese) 8 = actual/actual (ISMA) 9 = actual/360 (ISMA) 10 = actual/365 (ISMA) 11 = 30/360E (ISMA) 12 = actual/365 (ISDA)
`EndMonthRule`	(Optional) End-of-month rule. A vector. This rule applies only when `Maturity` is an end-of-month date for a month having 30 or fewer days. 0 = ignore rule, meaning that a bond's coupon payment date is always the same numerical day of the month. 1 = set rule on (default), meaning that a bond's coupon payment date is always the last actual day of the month.

Description

Price = zeroprice(Yield, Settle, Maturity, Period, Basis, EndMonthRule) calculates the prices for a portfolio of general short and long term zero-coupon instruments given the yield of the instruments. Price is a column vector containing a price for each zero-coupon instrument.

When there is less than one quasi-coupon, the function uses a simple yield based upon "Period times Number of Days in quasi coupon period" day-year. The default period is 2 and the default number of days is 180, which makes the user-supplied yield a simple yield on a 360-day year.

For longer term computations (more than one quasi-coupon), use the bond equivalent yield based upon present value (or compounding).

Formulas

To compute the price when there is 1 or 0 quasi-coupon periods to redemption, zeroprice uses the formula

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

The elements of the equations are defined as follows.

Variable	Definition
DSC	Number of days from settlement date to next quasi-coupon date as if the security paid periodic interest.
DSR	Number of days from settlement date to the redemption date (call date, put date, and so on).
E	Number of days in quasi-coupon period.
M	Number of quasi-coupon periods per year (standard for the particular security involved).
Nq	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.
Price	Dollar price per $100 par value.
RV	Redemption value.
Y	Annual yield (decimal) when held to redemption.

Examples

Example 1. Compute the price of a short-term zero-coupon instrument.

Settle = '24-Jun-1993';
Maturity = '1-Nov-1993';
Period = 2;
Basis = 0;
Yield = 0.04;

Price = zeroprice(Yield, Settle, Maturity, Period, Basis)  

Price =

   98.6066

Example 2. Compute the prices of a portfolio of two zero-coupon instruments, one short-term, and the other long-term.

Settle = '24-Jun-1993';
Maturity = ['01-Nov-1993'; '15-Jan-2024'];
Basis = [0; 1];
Yield = [0.04; 0.1];

Price = zeroprice(Yield, Settle, Maturity, [], Basis) 

Price =

   98.6066
    5.0697

References

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