Valuation of Convexity Related Derivatives

IES Working Paper No. 4/2008

27 Pages Posted: 14 May 2008 Last revised: 14 Jul 2017

See all articles by Jiri Witzany

Jiri Witzany

University of Economics in Prague

Date Written: March 2008

Abstract

We will investigate valuation of derivatives with payoff defined as a nonlinear though close to linear function of tradable underlying assets. Derivatives involving Libor or swap rates in arrears, i.e. rates paid in a wrong time, are a typical example. It is generally tempting to replace the future unknown interest rates with the forward rates. We will show rigorously that indeed this is not possible in the case of Libor or swap rates in arrears. We will introduce formally the notion of plain vanilla derivatives as those that can be replicated by a finite set of elementary operations and show that derivatives involving the rates in arrears are not plain vanilla. We will also study the issue of valuation of such derivatives. Beside the popular convexity adjustment formula we will develop an improved two or more variable adjustment formula applicable in particular on swap rates in arrears. Finally we will get a precise fully analytical formula based on the usual assumption of log-normality of the relevant tradable underlying assets applicable to a wide class of convexity related derivatives. We will illustrate the techniques and different results on a case study of a real life controversial exotic swap.

Keywords: interest rate derivatives, Libor in arrears, constant maturity swap

JEL Classification: C13, E43, E47, G13

Suggested Citation

Witzany, Jiri, Valuation of Convexity Related Derivatives (March 2008). IES Working Paper No. 4/2008. Available at SSRN: https://ssrn.com/abstract=1128227 or http://dx.doi.org/10.2139/ssrn.1128227

Jiri Witzany (Contact Author)

University of Economics in Prague ( email )

Winston Churchilla Sq. 4
Prague 3, 130 67
Czech Republic

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