lifecontingencies (version 1.3.9)

duration: Functions to evaluate duration and convexity

Description

These functions evaluate the duration or the convexity of a series of cash flows

Usage

duration(cashFlows, timeIds, i, k = 1, macaulay = TRUE)
convexity(cashFlows, timeIds, i, k = 1)

Value

A numeric value representing either the duration or the convexity of the cash flow series

Arguments

cashFlows

A vector representing the cash flows amounts.

timeIds

Cash flows times

i

APR interest, i.e. nominal interest rate compounded m-thly.

k

Compounding frequency for the nominal interest rate \(i\).

macaulay

Is the macaulay duration (default value) or the effective duration to be evaluated?

Author

Giorgio A. Spedicato

Details

The Macaulay duration is defined as \(\sum\limits_t^{T} \frac{t*CF_{t}\left( 1 + \frac{i}{k} \right)^{ - t*k}}{P}\), while \(\sum\limits_{t}^{T} t*\left( t + \frac{1}{k} \right) * CF_t \left(1 + \frac{y}{k} \right)^{ - k*t - 2}\)

References

Broverman, S.A., Mathematics of Investment and Credit (Fourth Edition), 2008, ACTEX Publications.

See Also

annuity

Examples

#evaluate the duration of a coupon payment
cf=c(10,10,10,10,10,110)
t=c(1,2,3,4,5,6)
duration(cf, t, i=0.03)
#and the convexity

convexity(cf, t, i=0.03)