Black-Scholes Formula in Subdiffusive Regime

@article{Magdziarz2009BlackScholesFI,
  title={Black-Scholes Formula in Subdiffusive Regime},
  author={Marcin Magdziarz},
  journal={Journal of Statistical Physics},
  year={2009},
  volume={136},
  pages={553-564}
}
In the classical approach the price of an asset is described by the celebrated Black-Scholes model. In this paper we consider a generalization of this model, which captures the subdiffusive characteristics of financial markets. We introduce a subdiffusive geometric Brownian motion as a model of asset prices exhibiting subdiffusive dynamics. We find the corresponding fractional Fokker-Planck equation governing the dynamics of the probability density function of the introduced process. We prove… CONTINUE READING

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