Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/78382
Authors: 
Zühlsdorff, Christian
Year of Publication: 
2002
Series/Report no.: 
Bonn Econ Discussion Papers 6/2002
Abstract: 
The market model of interest rates specifies simple forward or Libor rates as lognormally distributed, their stochastic dynamics has a linear volatility function. In this paper, the model is extended to quadratic volatility functions which are the product of a quadratic polynomial and a level-independent covariance matrix. The extended Libor market models allow for closed form cap pricing formulae, the implied volatilities of the new formulae are smiles and frowns. We give examples for the possible shapes of implied volatilities. Furthermore, we derive a new approximative swaption pricing formula and discuss its properties. The model is calibrated to market prices, it turns out that no extended model specification outperforms the others. The criteria for model choice should thus be theoretical properties and computational efficiency.
Subjects: 
forward Libor rates
Libor market model
affine volatility
quadratic volatility
dervatives pricing
closed form solutions
LMM
BGM
JEL: 
E43
G12
G13
Document Type: 
Working Paper

Files in This Item:
File
Size
359.31 kB





Items in EconStor are protected by copyright, with all rights reserved, unless otherwise indicated.