convexity

CNLMath : Special Functions : convexity

convexity

Synopsis

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>

int 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.