Valuation of convexity related derivatives

Arbeitspapier

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.

Angaben zum Objekt

• Sprache: Englisch

Verweise und Beziehungen

• Erschienen in: Series: IES Working Paper ; No. 4/2008

Klassifikation und Themen

• Klassifikation: Wirtschaft ; Estimation: General ; Interest Rates: Determination, Term Structure, and Effects ; Money and Interest Rates: Forecasting and Simulation: Models and Applications ; Contingent Pricing; Futures Pricing; option pricing
• Thema: interest rate derivatives ; Libor in arrears ; constant maturity swap ; valuation models ; convexity adjustment ; Derivat ; Zinsderivat ; Zinsderivat ; Theorie

Beteiligte, Orts- und Zeitangaben

• Ereignis: Geistige Schöpfung
• (wer): Witzany, Jiří
• Ereignis: Veröffentlichung
• (wer): Charles University in Prague, Institute of Economic Studies (IES)
• (wo): Prague
• (wann): 2008

Weitere Informationen

• Handle: http://hdl.handle.net/10419/83372
• Letzte Aktualisierung: 10.03.2025, 11:43 MEZ