In financial literature many have been the attempts to overcome the option pricing drawbacks that affect the Black and Scholes model. Starting from the Tsallis deformation of the usual exponential function, this paper presents, in a complete market setup, a class of deformed geometric Brownian motions flexible enough to reproduce fat tails and to capture the volatility behavior observed in models that consider both stochastic volatility and jumps.
Moretto, E., Pasquali, S., Trivellato, B. (2016). Option pricing under deformed Gaussian distributions. PHYSICA. A, 446(15 March 2016), 246-263 [10.1016/j.physa.2015.11.026].
Option pricing under deformed Gaussian distributions
MORETTO, ENRICO
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2016
Abstract
In financial literature many have been the attempts to overcome the option pricing drawbacks that affect the Black and Scholes model. Starting from the Tsallis deformation of the usual exponential function, this paper presents, in a complete market setup, a class of deformed geometric Brownian motions flexible enough to reproduce fat tails and to capture the volatility behavior observed in models that consider both stochastic volatility and jumps.
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