price¶

Evaluates the price, per $100 face value, of a security that pays periodic interest.

Synopsis¶

price (settlement, maturity, rate, t_yield, redemption, frequency, 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 rate (Input): Annual interest rate set forth on the face of the security; the coupon rate.
float t_yield (Input): Annual yield of the security.
float redemption (Input): Redemption value per $100 face value of the security.
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 on basis see the Usage Notes section of this chapter.

Return Value¶

The price per $100 face value of a security that pays periodic interest. If no result can be computed, NaN is returned.

Description¶

Function price computes the price per $100 face value of a security that pays periodic interest.It is computed using the following:

\[\left(\frac {\mathit{redemption}} {\left(1 + \frac{\mathit{yield}}{\mathit{freq}}\right)^{\left(N - 1 + \frac{\mathit{DSC}}{E}\right)}} \right) + \left[ \sum_{k=1}^{N} \frac {100 * \frac{\mathit{rate}}{\mathit{free}}} {\left(1 + \frac{\mathit{yield}}{\mathit{freq}}\right)^ {\left(k - 1 + \frac{\mathit{DSC}}{E}\right)}} \right]- \left( 100 * \frac{\mathit{rate}}{\mathit{freq}} * \frac{A}{E} \right)\]

In the above equation, DSC represents the number of days in the period 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 in the timeframe from the settlement date to the redemption date. A represents the number of days in the timeframe starting with the beginning of coupon period and ending with the settlement date.

Example¶

In this example, price computes the price of a bond that pays coupon every six months with the settlement of July 1, 1995, the maturity date of July 1, 2005, a annual rate of 6%, annual yield of 7% and redemption value of $105 using the US (NASD) 30/360 day count method.

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

rate = .06
yield_amt = .07
redemption = 105.
frequency = SEMIANNUAL
basis = DAY_CNT_BASIS_ACTUAL365

settlement = date(1995, 7, 1)
maturity = date(2005, 7, 1)

price_amt = price(settlement, maturity, rate, yield_amt,
                  redemption, frequency, basis)
print("The price of the bond is $%.2f." % (price_amt))

Output¶

The price of the bond is $95.41.