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Price zero-coupon instruments given yield


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



Price = zeroprice(Yield,Settle,Maturity) prices zero-coupon instruments given a yield. 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.


Price = zeroprice(___,Period,Basis,EndMonthRule) adds optional arguments for Period, Basis, and EndMonthRule.


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This example shows how to 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

This example shows how to 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 = 2×1


Input Arguments

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Reference bond yield, specified as a scalar or a NZERO-by-1 vector.

Data Types: double

Settlement date, specified as a NZERO-by-1 vector of serial date numbers.

Data Types: double

Maturity date, specified as a NZERO-by-1 vector of serial date numbers.

Data Types: double

(Optional) Number of coupons in one year, specified as a positive integer for the values 1,2,4,6,12 in a NZERO-by-1 vector.

Data Types: double

(Optional) Day-count basis of the bond, specified as a positive integer using a NZERO-by-1 vector.

  • 0 = actual/actual

  • 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 (ICMA)

  • 9 = actual/360 (ICMA)

  • 10 = actual/365 (ICMA)

  • 11 = 30/360E (ICMA)

  • 12 = actual/365 (ISDA)

  • 13 = BUS/252

For more information, see basis.

Data Types: double

(Optional) End-of-month rule flag, specified as a nonnegative integer with a value of 0 or 1 using a NZERO-by-1 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 coupon payment date is always the same numerical day of the month.

  • 1 = Set rule on, meaning that a bond coupon payment date is always the last actual day of the month.

Data Types: double

Output Arguments

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Price for each zero-coupon instrument (per $100 notional), returned as a column vector.


To compute the price when Period is 1 or 0 for the 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.



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.

Introduced before R2006a