8 papers
From constant to rough: A survey of continuous volatility modeling
Giulia Di Nunno, KÄstutis Kubilius, Yuliya Mishura +1
In this paper, we present a comprehensive survey of continuous stochastic volatility models, discussing their historical development and the key stylized facts that have driven the…
Properties of the Shannon, Rényi and other entropies: dependence in parameters, robustness in distributions and extremes
Iryna Bodnarchuk, Yuliya Mishura, Kostiantyn Ralchenko
We calculate and analyze various entropy measures and their properties for selected probability distributions. The entropies considered include Shannon, Rényi, generalized Rényi,…
Gaussian Volterra processes as models of electricity markets
Yuliya Mishura, Stefania Ottaviano, Tiziano Vargiolu
We introduce a non-Markovian model for electricity markets where the spot price of electricity is driven by several Gaussian Volterra processes, which can be e.g., fractional Brown…
Driven by Brownian motion Cox-Ingersoll-Ross and squared Bessel processes: interaction and phase transition
Yuliya Mishura, Kostiantyn Ralchenko, Svitlana Kushnirenko
This paper studies two related stochastic processes driven by Brownian motion: the Cox-Ingersoll-Ross (CIR) process and the Bessel process. We investigate their shared and distinct…
Fractional Gaussian noise: Projections, prediction, norms
Iryna Bodnarchuk, Yuliya Mishura, Kostiantyn Ralchenko
We examine the one-sided and two-sided (bilateral) projections of an element of fractional Gaussian noise onto its neighboring elements. We establish several analytical results and…
Option pricing in Sandwiched Volterra Volatility model
Giulia Di Nunno, Yuliya Mishura, Anton Yurchenko-Tytarenko
We introduce a new model of financial market with stochastic volatility driven by an arbitrary Hölder continuous Gaussian Volterra process. The distinguishing feature of the model…