convexity¶

Evaluates the convexity for a security.

Synopsis¶

convexity (settlement, maturity, couponRate, t_yield, 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 couponRate (Input): Annual interest rate set forth on the face of the security; the coupon rate.
float t_yield (Input): Annual yield 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 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 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:

\[\frac {\displaystyle\frac{1}{(q * \mathit{frequency})^2} \left\{ \displaystyle\sum_{t=1}^{n}t(t+1) \left(\frac{\mathit{rate}}{\mathit{frequency}}\right)q^{-t} + n(n+1)q^{-n} \right\}} {\displaystyle\sum_{t=1}^{n}\left(\frac{\mathit{rate}}{\mathit{frequency}}\right)q^{-t} + q^{-n}}\]

where n is calculated from couponNumber, and \(q=1+\tfrac{\mathit{yield}}{\mathit{frequency}}\).

Example¶

In this example, 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.

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

coupon = .075
yield_val = .09
frequency = SEMIANNUAL
basis = DAY_CNT_BASIS_ACTUAL365

settlement = date(1990, 7, 1)
maturity = date(2000, 7, 1)

convexity_value = convexity(settlement, maturity,
                            coupon, yield_val, frequency, basis)
print("The convexity of the bond with", end=' ')
print("semiannual interest payments is %.4f." % (convexity_value))

Output¶

The convexity of the bond with semiannual interest payments is 59.4050.