Evaluates the convexity for a security.
Synopsis
#include <imsl.h>
float
imsl_f_convexity (struct
tm settlement, struct
tm maturity,
float coupon_rate, float yield, int frequency, int basis)
The type double function is imsl_d_convexity.
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 convexity for a security. If no result can be computed, NaN is returned.
Description
Function imsl_f_convexity computes the convexity for a security. Convexity is the sensitivity of the duration of a security to changes in yield.
It is computed using the following:
where n is calculated from imsl_coupon_number,
and 
.
Example
In this example, imsl_f_convexity computes the convexity for a security with the settlement date of July 1, 1990, and maturity date of July 1, 2000, 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 convexity;
settlement.tm_year = 90;
settlement.tm_mon = 6;
settlement.tm_mday = 1;
maturity.tm_year = 100;
maturity.tm_mon = 6;
maturity.tm_mday = 1;
convexity = imsl_f_convexity (settlement, maturity,
coupon, yield, frequency, basis);
printf ("The convexity of the bond with ");
printf ("semiannual interest payments is %.4f.\n", convexity);
}
Output
The convexity of the bond with semiannual interest payments is 59.4050.
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