Evaluates the annual duration of a security where the security has periodic interest payments.
Synopsis
#include <imsl.h>
float
imsl_f_duration (struct
tm settlement, struct
tm maturity,
float coupon_rate, float yield, int frequency, int basis)
The type double function is imsl_d_duration.
Required Arguments
struct tm
settlement (Input)
The date on which payment is made to
settle a trade. For a more detailed discussion on dates see the Usage Notes section of
this chapter.
struct tm maturity
(Input)
The date on which the bond comes due, and principal and accrued
interest are paid. For a more detailed discussion on dates see the Usage Notes section of
this chapter.
float
coupon_rate (Input)
Annual interest rate set forth on the
face of the security; the coupon rate.
float yield
(Input)
Annual yield of the security.
int frequency
(Input)
Frequency of the interest payments. It should be one of
IMSL_ANNUAL,
IMSL_SEMIANNUAL
or IMSL_QUARTERLY. For a
more detailed discussion on frequency see
the Usage Notes
section of this chapter.
int basis
(Input)
The method for computing the number of days between two dates. It
should be one of IMSL_DAY_CNT_BASIS_ACTUALACTUAL,
IMSL_DAY_CNT_BASIS_NASD,
IMSL_DAY_CNT_BASIS_ACTUAL360,
IMSL_DAY_CNT_BASIS_ACTUAL365,
or IMSL_DAY_CNT_BASIS_30E360.
For a more detailed discussion see the Usage Notes section of this
chapter.
Return Value
The annual duration of a security with periodic interest payments. If no result can be computed, NaN is returned.
Description
Function imsl_f_duration computes the Maccaluey's duration of a security with periodic interest payments. The Maccaluey's duration is the weighted-average time to the payments, where the weights are the present value of the payments.
It is computed using the following:
In the equation above, DSC represents the number of days starting with the settlement date and ending with the next coupon date. E represents the number of days within the coupon period. N represents the number of coupons payable from the settlement date to the maturity date. freq represents the frequency of the coupon payments annually.
Example
In this example, imsl_f_duration computes the annual duration of a security with the settlement date of July 1, 1995, and maturity date of July 1, 2005, using the Actual/365 day count method.
#include <stdio.h>
#include "imsl.h"
void main()
{
struct tm settlement, maturity;
float coupon = .075;
float yield = .09;
int frequency = IMSL_SEMIANNUAL;
int basis = IMSL_DAY_CNT_BASIS_ACTUAL365;
float duration;
settlement.tm_year = 95;
settlement.tm_mon = 6;
settlement.tm_mday = 1;
maturity.tm_year = 105;
maturity.tm_mon = 6;
maturity.tm_mday = 1;
duration = imsl_f_duration (settlement, maturity, coupon,
yield, frequency, basis);
printf ("The annual duration of the bond with ");
printf ("semiannual interest payments is %.4f.\n", duration);
}
Output
The annual duration of the bond with semiannual interest payments is 7.0420.
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