duration

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>

 

int 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.