Template-Type: ReDIF-Paper 1.0
Title: The Pricing of Derivatives on Assets with Quadratic Volatility 
Author-Name: Christian Zühlsdorff 
Author-Email: 
Classification-JEL: G12, G13 
Keywords: strong solutions, stochastic differential equation, option pricing, quadratic volatility, implied volatility, smiles, frowns 
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's volatility is a linear function of the asset value and the model garantees positive asset prices. In this paper it is shown that 
	the pricing partial differential equation can be solved for level-dependent volatility which is a quadratic polynomial. If zero is attainable, both absorption and 
	negative asset values are possible. Explicit formulae are derived for the call option: a generalization of the Black-Scholes formula for an asset whose volatiliy is 
	affine, the formula for the Bachelier model with constant volatility, and new formulae in the case of quadratic volatility. The implied Black-Scholes volatilities 
	of the Bachelier and the affine model are frowns, the quadratic specifications imply smiles. 
Note: 
Length: 29
Creation-Date: 2002-01	
Revision-Date: 
File-URL: http://www.wiwi.uni-bonn.de/bgsepapers/bonedp/bgse5_2002.pdf
File-Format: application/pdf
Handle: RePEc:bon:bonedp:bgse5_2002