69 citations · 127 across the 4 of their papers we have counts for
7 papers
Equity warrant pricing under subdiffusive fractional Brownian motion of the short rate
Foad Shokrollahi, Marcin Marcin Magdziarz
In this paper we propose an extension of the Merton model. We apply the subdiffusive mechanism to analyze equity warrant in a fractional Brownian motion environment, when the short…
First passage time moments of asymmetric Lévy flights
Amin Padash, Aleksei V. Chechkin, Bartłomiej Dybiec +3
We investigate the first-passage dynamics of symmetric and asymmetric Lévy flights in a semi-infinite and bounded intervals. By solving the space-fractional diffusion equation, we…
A computational weighted finite difference method for American and barrier options in subdiffusive Black-Scholes model
Grzegorz Krzyżanowski, Marcin Magdziarz
Subdiffusion is a well established phenomenon in physics. In this paper we apply the subdiffusive dynamics to analyze financial markets. We focus on the financial aspect of time fr…
A weighted finite difference method for subdiffusive Black Scholes Model
Grzegorz Krzyżanowski, Marcin Magdziarz, Łukasz Płociniczak
In this paper we focus on the subdiffusive Black Scholes model. The main part of our work consists of the finite difference method as a numerical approach to the option pricing in…
Codifference can detect ergodicity breaking and non-Gaussianity
Jakub Slezak, Ralf Metzler, Marcin Magdziarz
We show that the codifference is a useful tool in studying the ergodicity breaking and non-Gaussianity properties of stochastic time series. While the codifference is a measure of…
Superstatistical generalised Langevin equation: non-Gaussian viscoelastic anomalous diffusion
Jakub Ślęzak, Ralf Metzler, Marcin Magdziarz
Recent advances in single particle tracking and supercomputing techniques demonstrate the emergence of normal or anomalous, viscoelastic diffusion in conjunction with non-Gaussian…