Template-Type: ReDIF-Paper 1.0
Title: Extended Libor Market Models with Affine and Quadratic Volatility 
Author-Name: Christian Zühlsdorff 
Author-Email: 
Classification-JEL: E43, G12, G13 
Keywords: forward Libor rates, Libor market model, affine volatility, quadratic volatility, dervatives pricing, closed form solutions, LMM, BGM 
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. 
Note: 
Length: 28
Creation-Date: 2002-01	
Revision-Date: 
File-URL: http://www.wiwi.uni-bonn.de/bgsepapers/bonedp/bgse6_2002.pdf
File-Format: application/pdf
Handle: RePEc:bon:bonedp:bgse6_2002