Original Research

Adapting the Macaulay duration for defaultable and option-embedded bonds

Gary Wayne van Vuuren, Paul Styger
South African Journal of Economic and Management Sciences | Vol 11, No 2 | a307 | DOI: https://doi.org/10.4102/sajems.v11i2.307 | © 2011 Gary Wayne van Vuuren, Paul Styger | This work is licensed under CC Attribution 4.0
Submitted: 27 September 2011 | Published: 28 September 2011

About the author(s)

Gary Wayne van Vuuren, North West University & Fitch Ratings, UK, United Kingdom
Paul Styger, North West University

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Most contemporary bonds have embedded options and all face the possibility of default. Both features introduce risk (the former market risk and the latter credit risk) by altering the quantity and timing of the promised cash flows. The Macaulay duration, although a popular risk tool, is increasingly unable to cope in this complex financial environment. While the Macaulay duration has undergone modifications before, a new theoretical framework is now introduced which augments its functionality while retaining its tractability. The approach – though still unable to isolate the effects of the two features – yields consistent results which agree well with empirical data.


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