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The Pricing of Derivatives on Assets with Quadratic Volatility


Christian Zühlsdorff


University of Bonn - Institute of Statistics

March 1999

SFB 303 Working Paper No. B - 451

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 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.

Number of Pages in PDF File: 10

JEL Classification: G12, G13

working papers series


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Date posted: November 17, 1999  

Suggested Citation

Zühlsdorff, Christian, The Pricing of Derivatives on Assets with Quadratic Volatility (March 1999). SFB 303 Working Paper No. B - 451. Available at SSRN: http://ssrn.com/abstract=182773 or http://dx.doi.org/10.2139/ssrn.182773

Contact Information

Christian Zühlsdorff (Contact Author)
University of Bonn - Institute of Statistics ( email )
Adenauerallee 24-26
Bonn, 53113
Germany
+49 228 739268 (Phone)
+49 228 725050 (Fax)
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