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.

VariableDefinition

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.

See Also

bndprice, cdprice, tbillprice, zeroyield

  


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