Valuation of Convexity Related Derivatives

Jiří Witzany

No 2008/04, Working Papers IES from Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies

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; valuation models; convexity adjustment (search for similar items in EconPapers)
JEL-codes: C13 E43 E47 G13 (search for similar items in EconPapers)
Pages: 22 pages
Date: 2008-03, Revised 2008-03
New Economics Papers: this item is included in nep-fmk and nep-mac
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