accrInterestPeriodic¶

Evaluates the interest which has accrued on a security that pays interest periodically.

Synopsis¶

accrInterestPeriodic (issue, firstCoupon, settlement, couponRate, parValue, frequency, basis)

Required Arguments¶

date issue (Input): The date on which interest starts accruing. For a more detailed discussion on dates see the Usage Notes section of this chapter.
date firstCoupon (Input): First date on which an interest payment is due on the security (e.g., the coupon date). For a more detailed discussion on dates see the Usage Notes section of this chapter.
date 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.
float couponRate (Input): Annual interest rate set forth on the face of the security; the coupon rate.
float parValue (Input): Nominal or face value of the security used to calculate interest payments.
int frequency (Input): Frequency of the interest payments. It should be one of ANNUAL, SEMIANNUAL or 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 DAY_CNT_BASIS_ACTUALACTUAL, DAY_CNT_BASIS_NASD, DAY_CNT_BASIS_ACTUAL360, DAY_CNT_BASIS_ACTUAL365, or DAY_CNT_BASIS_30E360. For a more detailed discussion see the Usage Notes section of this chapter.

Return Value¶

The accrued interest for a security that pays periodic interest. If no result can be computed, NaN is returned.

Description¶

Function accrInterestPeriodic computes the accrued interest for a security that pays periodic interest.

In the equation below, $A_i$ represents the number of days which have accrued for the i-th quasi-coupon period within the odd period. (The quasi-coupon periods are periods obtained by extending the series of equal payment periods to before or after the actual payment periods.) NC represents the number of quasi-coupon periods within the odd period, rounded to the next highest integer. (The odd period is a period between payments that differs from the usual equally spaced periods at which payments are made.) $NL_i$ represents the length of the normal i-th quasi-coupon period within the odd period. $NL_i$ is expressed in days.

Function accrInterestPeriodic can be found by solving the following:

\[(\mathit{parValue})\left( \frac{\mathit{rate}}{\mathit{frequency}} \left[ \sum_{\mathrm{i}=1}^{\mathrm{NC}} \left(\frac{A_{\mathrm{i}}}{NL_{\mathrm{i}}}\right) \right] \right)\]

Example¶

In this example, accrInterestPeriodic computes the accrued interest for a security that pays periodic interest using the US (NASD) 30/360 day count method. The security has a par value of $1,000, the issue date of October 1, 1999, the settlement date of November 3, 1999, the first coupon date of March 31, 2000, and a coupon rate of 6%.

from __future__ import print_function
from numpy import *
from datetime import date
from pyimsl.math.accrInterestPeriodic import accrInterestPeriodic, DAY_CNT_BASIS_NASD, SEMIANNUAL

rate = .06
par = 1000.
frequency = SEMIANNUAL
basis = DAY_CNT_BASIS_NASD

issue = date(1999, 10, 1)
first_coupon = date(2000, 3, 31)
settlement = date(1999, 11, 3)

accrint = accrInterestPeriodic(issue, first_coupon,
                               settlement, rate, par, frequency, basis)
print("The accrued interest is $%.2f." % (accrint))

Output¶

The accrued interest is $5.33.