Price zero-coupon instruments given yield
zero-coupon instruments given a yield.
Price = zeroprice(
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.
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 98.6066 5.0697
Yield— Reference bond yield
Reference bond yield, specified as a scalar or a
Settle— Settlement date
Settlement date, specified as a
of serial date numbers.
Maturity— Maturity date
Maturity date, specified as a
of serial date numbers.
Period— Number of coupons in one year
2(semiannual) (default) | vector of positive integers from the set
(Optional) Number of coupons in one year, specified as a positive
integer for the values
1,2,4,6,12 in a
Basis— Day-count basis of bond
0(actual/actual) (default) | vector of positive integers of the set
(Optional) Day-count basis of the bond, specified as a positive
integer using a
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.
EndMonthRule— End-of-month rule flag
1(in effect) (default) | nonnegative integer with value of
(Optional) End-of-month rule flag, specified as a nonnegative
integer with a value of
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.
Price— Price for each zero-coupon instrument
Price for each zero-coupon instrument (per $100 notional), returned as a column vector.
To compute the price when
the quasi-coupon periods to redemption,
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
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.
Annual yield (decimal) when held to redemption.
 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.