Arbeitspapier
The Pricing of Derivatives on Assets with Quadratic Volatility
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.
- Sprache
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Englisch
- Erschienen in
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Series: Bonn Econ Discussion Papers ; No. 5/2002
- Klassifikation
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Wirtschaft
Asset Pricing; Trading Volume; Bond Interest Rates
Contingent Pricing; Futures Pricing; option pricing
- Thema
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strong solutions
stochastic differential equation
option pricing
quadratic volatility
implied volatility
smiles
frowns
- Ereignis
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Geistige Schöpfung
- (wer)
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Zühlsdorff, Christian
- Ereignis
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Veröffentlichung
- (wer)
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University of Bonn, Bonn Graduate School of Economics (BGSE)
- (wo)
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Bonn
- (wann)
-
2002
- Handle
- Letzte Aktualisierung
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10.03.2025, 11:43 MEZ
Datenpartner
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Objekttyp
- Arbeitspapier
Beteiligte
- Zühlsdorff, Christian
- University of Bonn, Bonn Graduate School of Economics (BGSE)
Entstanden
- 2002
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