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Valuation of Convexity Related Interest Rate Derivatives

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Author Info

  • Jiří Witzany

Abstract

We investigate valuation of derivatives with payoff defined as a nonlinear though close to linear function of tradable underlying assets. Interest rate derivatives involving Libor or swap rates in arrears, i.e. rates paid at wrong time, are a typical example. It is generally tempting to replace the future unknown interest rates with the forward rates. We show rigorously that indeed this is not possible in the case of Libor or swap rates in arrears. We introduce formally the notion of linear 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 (linear) plain vanilla. We also study the issue of valuation of such derivatives. Beside the popular convexity adjustment formula, we develop an improved two or more variable adjustment formula applicable in particular on swap rates in arrears. Finally, we 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 illustrate the techniques and different results on a case study of a real life controversial exotic swap.

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Bibliographic Info

Article provided by University of Economics, Prague in its journal Prague Economic Papers.

Volume (Year): 2009 (2009)
Issue (Month): 4 ()
Pages: 309-326

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Handle: RePEc:prg:jnlpep:v:2009:y:2009:i:4:id:356:p:309-326

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Related research

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

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References

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  1. Henrard, Marc, 2007. "CMS swaps in separable one-factor Gaussian LLM and HJM model," MPRA Paper 3228, University Library of Munich, Germany.
  2. Eric Benhamou, 2000. "Pricing Convexity Adjustment with Wiener Chaos," FMG Discussion Papers dp351, Financial Markets Group.
  3. A. Pelsser, 2003. "Mathematical foundation of convexity correction," Quantitative Finance, Taylor & Francis Journals, vol. 3(1), pages 59-65.
  4. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  5. Martin Vojtek, 2004. "Calibration of Interest Rate Models - Transition Market Case," Finance 0410015, EconWPA.
  6. Eric Benhamou, 2002. "A Martingale Result for Convexity Adjustment in the Black Pricing Model," Finance 0212005, EconWPA.
  7. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
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Cited by:
  1. Martin Pohl, 2012. "Czech Swap Market in the Crisis Period," Prague Economic Papers, University of Economics, Prague, vol. 2012(1), pages 101-122.

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