English, Article, Journal or magazine article edition: The Pricing of Derivatives on Assets with Quadratic Volatility Christian Zuehlsdorff

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Bookmark: http://trove.nla.gov.au/version/52132
Physical Description
  • preprint
Language
  • English

Edition details

Title
  • The Pricing of Derivatives on Assets with Quadratic Volatility
Author
  • Christian Zuehlsdorff
Physical Description
  • preprint
Notes
  • 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.
  • option pricing, quadratic volatility, volatility smiles
  • RePEc:bon:bonsfb:451
Language
  • English
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