Valuation of Convexity Related Derivatives
AbstractWe 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.
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Bibliographic InfoPaper provided by Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies in its series Working Papers IES with number 2008/04.
Length: 22 pages
Date of creation: Mar 2008
Date of revision: Mar 2008
interest rate derivatives; Libor in arrears; constant maturity swap; valuation models; convexity adjustment;
Find related papers by 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
This paper has been announced in the following NEP Reports:
- NEP-ALL-2008-03-15 (All new papers)
- NEP-FMK-2008-03-15 (Financial Markets)
- NEP-MAC-2008-03-15 (Macroeconomics)
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