lifecontingencies (version 1.3.12)

duration: Compute the duration or the convexity of a series of CF

Description

Compute the duration or the convexity of a series of CF

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.

macaulay

Use the Macaulay formula

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.

Examples

#evaluate the duration/convexity 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)
convexity(cf, t, i=0.03)