50 citations · 119 across the 14 of their papers we have counts for
14 papers
Modeling interest rate swap volatility with GARCH processes
Michał Balcerek, Michał Wronka
We examine the conditional volatility dynamics of the USD 1Yx10Y forward swap rate using GARCH(1,1), GJR-GARCH(1,1), and a two-regime Markov-switching GARCH (MSGARCH) model. The an…
Turning angle analysis reveals hidden anisotropies in intracellular transport
Michał Balcerek, Adrian Pacheco-Pozo, Agnieszka Wyłomańska +1
Molecular motion within living cells provides a window into the physical principles underlying intracellular organization and transport. Yet a fundamental limitation remains: measu…
Machine learning models for predicting catastrophe bond coupons using climate data
Julia Kończal, Michał Balcerek, Krzysztof Burnecki
In recent years, the growing frequency and severity of natural disasters have increased the need for effective tools to manage catastrophe risk. Catastrophe (CAT) bonds allow the t…
Two-dimensional fractional Brownian motion: Analysis in time and frequency domains
Michał Balcerek, Adrian Pacheco-Pozo, Agnieszka Wyłomańska +2
This article introduces a novel construction of the two-dimensional fractional Brownian motion (2D fBm) with dependent components. Unlike similar models discussed in the literature…
Multifractional Brownian motion with telegraphic, stochastically varying exponent
Michał Balcerek, Samudrajit Thapa, Krzysztof Burnecki +4
The diversity of diffusive systems exhibiting long-range correlations characterized by a stochastically varying Hurst exponent calls for a generic multifractional model. We present…
CINNAMON: A hybrid approach to change point detection and parameter estimation in single-particle tracking data
Jakub Malinowski, Marcin Kostrzewa, Michał Balcerek +2
Change point detection has become an important part of the analysis of the single-particle tracking data, as it allows one to identify moments, in which the motion patterns of obse…
Evaluating Gaussianity of heterogeneous fractional Brownian motion
Michał Balcerek, Adrian Pacheco-Pozo, Agnieszka Wyłomańska +1
Heterogeneous diffusion processes are prevalent in various fields, including the motion of proteins in living cells, the migratory movement of birds and mammals, and finance. These…
Two-dimensional Brownian motion with dependent components: turning angle analysis
Michał Balcerek, Adrian Pacheco-Pozo, Agnieszka Wyłomanska +2
Brownian motion in one or more dimensions is extensively used as a stochastic process to model natural and engineering signals, as well as financial data. Most works dealing with m…
Langevin equation in heterogeneous landscapes: how to choose the interpretation
Adrian Pacheco-Pozo, Michał Balcerek, Agnieszka Wyłomańska +3
The Langevin equation is a common tool to model diffusion at a single-particle level. In non-homogeneous environments, such as aqueous two-phase systems or biological condensates w…
Modelling intermittent anomalous diffusion with switching fractional Brownian motion
Michał Balcerek, Agnieszka Wyłomańska, Krzysztof Burnecki +2
The stochastic trajectories of molecules in living cells, as well as the dynamics in many other complex systems, often exhibit memory in their path over long periods of time. In ad…
Memory-multi-fractional Brownian motion with continuous correlations
Wei Wang, Michal Balcerek, Krzysztof Burnecki +6
We propose a generalization of the widely used fractional Brownian motion (FBM), memory-multi-FBM (MMFBM), to describe viscoelastic or persistent anomalous diffusion with time-depe…
Fractional Brownian motion with random Hurst exponent: accelerating diffusion and persistence transitions
Michał Balcerek, Krzysztof Burnecki, Samudrajit Thapa +2
Fractional Brownian motion, a Gaussian non-Markovian self-similar process with stationary long-correlated increments, has been identified to give rise to the anomalous diffusion be…
About subordinated generalizations of 3 classical models of option pricing
Michał Balcerek, Grzegorz Krzyżanowski, Marcin Magdziarz
In this paper, we investigate the relation between Bachelier and Black-Scholes models driven by the infinitely divisible inverse subordinators. Such models, in contrast to their cl…
Testing of fractional Brownian motion in a noisy environment
Michal Balcerek, Krzysztof Burnecki
Fractional Brownian motion (FBM) is the only Gaussian self-similar process with stationary increments. Its increment process, called fractional Gaussian noise, is ergodic and exhib…