Saturday, November 28, 2020

Waring offers new paper assisting generalists in calculating durations and convexities, including dual durations, for perpetuities, annuities, zero coupon bonds, and coupon bonds 

In this reference note, intended for relatively easy use by finance generalists, we derive the formulae for a) the prices and dual and single durations and convexities for b) growing and nominal instruments, including c) coupon bonds, zero coupon bonds, annuities, and perpetuities, across d) the seven most useful and relevant combinations of coupon, discounting, and other cash flow details (forms)—all in a relatively compact form of presentation. These forms include 7 variations of continuous or discrete coupons, payment timing [i.e., payments made at the end of the period (most common) or payments made at the beginning of the period (annuity due)], growth beginning right away during the first period, or growth only beginning during the second period (the conventional form for most growing perpetuities and annuities), and continuous or discrete compounding.

This is ambitious; that’s a big delivery from a paper of only modestly excessive length— There are solutions for four types of fixed income instruments, each solving for either real or nominal values, across seven forms for growing instruments and five for nominal instruments; that’s 48 different solutions for duration and convexity. Not all are equally useful, but many are very much so.  Click here to read