26 citations · 60 across the 14 of their papers we have counts for
14 papers
Power law in Sandwiched Volterra Volatility model
Giulia Di Nunno, Anton Yurchenko-Tytarenko
In this paper, we present analytical proof demonstrating that the Sandwiched Volterra Volatility (SVV) model is able to reproduce the power-law behavior of the at-the-money implied…
From constant to rough: A survey of continuous volatility modeling
Giulia Di Nunno, Kęstutis 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…
Parameter estimation in rough Bessel model
Yuliya Mishura, Anton Yurchenko-Tytarenko
In this paper, we construct consistent statistical estimators of the Hurst index, volatility coefficient, and drift parameter for Bessel processes driven by fractional Brownian mot…
Low-dimensional Cox-Ingersoll-Ross process
Yuliya Mishura, Andrey Pilipenko, Anton Yurchenko-Tytarenko
The present paper investigates Cox-Ingersoll-Ross (CIR) processes of dimension less than 1, with a focus on obtaining an equation of a new type including local times for the square…
Sandwiched Volterra Volatility model: Markovian approximations and hedging
Giulia Di Nunno, Anton Yurchenko-Tytarenko
We consider stochastic volatility dynamics driven by a general Hölder continuous Volterra-type noise and with unbounded drift. For these so-called SVV-models, we consider the expli…
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…
Drift-implicit Euler scheme for sandwiched processes driven by Hölder noises
Giulia Di Nunno, Yuliya Mishura, Anton Yurchenko-Tytarenko
In this paper, we analyze the drift-implicit (or backward) Euler numerical scheme for a class of stochastic differential equations with unbounded drift driven by an arbitrary -H…
Standard and fractional reflected Ornstein-Uhlenbeck processes as the limits of square roots of Cox-Ingersoll-Ross processes
Yuliya Mishura, Anton Yurchenko-Tytarenko
In this paper, we establish a new connection between Cox-Ingersoll-Ross (CIR) and reflected Ornstein-Uhlenbeck (ROU) models driven by either a standard Wiener process or a fraction…
Optimal control in linear stochastic advertising models with memory
Michele Giordano, Anton Yurchenko-Tytarenko
This paper deals with a class of optimal control problems which arises in advertising models with Volterra Ornstein-Uhlenbeck process representing the product goodwill. Such choice…
Sandwiched SDEs with unbounded drift driven by Hölder noises
Giulia Di Nunno, Yuliya Mishura, Anton Yurchenko-Tytarenko
We study a stochastic differential equation with an unbounded drift and general Hölder continuous noise of an arbitrary order. The corresponding equation turns out to have a unique…
Fractional Cox--Ingersoll--Ross process with small Hurst indices
Yuliya Mishura, Anton Yurchenko-Tytarenko
In this paper the fractional Cox-Ingersoll-Ross process on for is defined as a square of a pointwise limit of the processes , satisfying the…
Option pricing in fractional Heston-type model
Yuliya Mishura, Anton Yurchenko-Tytarenko
In this paper, we consider option pricing in a framework of the fractional Heston-type model with . As it is impossible to obtain an explicit formula for the expectation $\m…
Fractional Cox--Ingersoll--Ross process with non-zero <<mean>>
Yuliya Mishura, Anton Yurchenko-Tytarenko
In this paper we define the fractional Cox-Ingersoll-Ross process as , where the process satisfies the SDE of the…
Stochastic representation and pathwise properties of fractional Cox-Ingersoll-Ross process
Yuliya Mishura, Vladimir I. Piterbarg, Kostiantyn Ralchenko +1
We consider the fractional Cox-Ingersoll-Ross process satisfying the stochastic differential equation (SDE) driven by a fractional Brownian…