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

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Bookmark: http://trove.nla.gov.au/version/52275
Physical Description
  • preprint
Language
  • English

Edition details

Title
  • The Pricing of Derivatives on Assets with Quadratic Volatility
Author
  • Christian Zühlsdorff
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'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.
  • strong solutions, stochastic differential equation, option pricing, quadratic volatility, implied volatility, smiles, frowns
  • RePEc:bon:bonedp:bgse5_2002
Language
  • English
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