Template-Type:ReDIF-Paper 1.0  
Title:  The Pricing of Derivatives on Assets with Quadratic Volatility
Author-Name:  Christian Zuehlsdorff 
Classification-JEL: G13
Keywords:  option pricing, quadratic volatility, volatility smiles
Abstract:  The basic model of financial economics is the Samuelson model of geometric 
   Brownian motion because of the celebrated Black-Scholes formula for pricing the 
   call option. The asset volatility is a linear function of the asset value and the
   model guarantees positive asset prices. We show that the the pricing PDE can be 
   solved if the volatility function is a quadratic polynomial and give explicit 
   formulas for the call option: a generalization of the Black-Scholes formula for 
   an asset whose volatility is affine, a formula for the Bachelier model with constant 
   volatility and a new formula in the case of quadratic volatility. The implied 
   Black-Scholes volatilities of the Bachelier and the affine model are frowns, 
   the quadratic specifications also imply smiles. 
Length: pages
Creation-Date: 1999-03
Revision-Date: 
Handle: RePEc:bon:bonsfb:451
File-URL: http://www.wiwi.uni-bonn.de/bgsepapers/bonsfb/bonsfb451.pdf
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