discountRate¶

Evaluates the interest rate implied when a security is sold for less than its value at maturity in lieu of interest payments.

Synopsis¶

discountRate (settlement, maturity, price, redemption, basis)

Required Arguments¶

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.
date 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 price (Input): Price per $100 face value of the security.
float redemption (Input): Redemption value per $100 face value of the security.
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 discount rate for a security. If no result can be computed, NaN is returned.

Description¶

Function discountRate computes the discount rate for a security. The discount rate is the interest rate implied when a security is sold for less than its value at maturity in lieu of interest payments.

It is computed using the following:

\[\left(\frac{\mathit{redemption} - \mathit{price}}{\mathit{price}}\right) \left(\frac{B}{\mathit{DSM}}\right)\]

In the equation above, B represents the number of days in a year based on the annual basis and DSM represents the number of days starting with the settlement date and ending with the maturity date.

Example¶

In this example, discountRate computes the discount rate of a security which is selling at $97.975 with the settlement date of February 15, 2000, and maturity date of June 10, 2000, using the Actual/365 day count method.

from __future__ import print_function
from numpy import *
from datetime import date
from pyimsl.math.discountRate import discountRate, DAY_CNT_BASIS_ACTUAL365

price = 97.975
redemption = 100.0
basis = DAY_CNT_BASIS_ACTUAL365

settlement = date(2000, 2, 15)
maturity = date(2000, 6, 10)

rate = discountRate(settlement, maturity, price,
                    redemption, basis)
print("The discount rate for the security is %.2f%%." % (rate * 100))

Output¶

The discount rate for the security is 6.37%.