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Valuation of Convexity Related Derivatives

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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.

Suggested Citation

  • Jiří Witzany, 2008. "Valuation of Convexity Related Derivatives," Working Papers IES 2008/04, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, revised Mar 2008.
  • Handle: RePEc:fau:wpaper:wp2008_04
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    File URL: http://ies.fsv.cuni.cz/default/file/download/id/8780
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    1. Dharmapala, Dhammika, 2003. "Budgetary Policy with Unified and Decentralized Appropriations Authority," Public Choice, Springer, vol. 115(3-4), pages 347-367, June.
    2. Balassone, Fabrizio & Giordano, Raffaela, 2001. "Budget Deficits and Coalition Governments," Public Choice, Springer, vol. 106(3-4), pages 327-349, March.
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    Keywords

    interest rate derivatives; Libor in arrears; constant maturity swap; valuation models; convexity adjustment;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • E47 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Forecasting and Simulation: Models and Applications
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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