Related papers: A comparison between several correlated stochastic…

Here we propose two alternatives to Black 76 to value European option future contracts in which the underlying market prices can be negative or mean reverting. The two proposed models are Ornstein-Uhlenbeck (OU) and continuous time GARCH…

We perform a classification of the Lie point symmetries for the Black--Scholes--Merton Model for European options with stochastic volatility, $\sigma$, in which the last is defined by a stochastic differential equation with an…

We price European options in a class of models in which the volatility of the underlying risky asset depends on the short rate of interest. Our study results in an explicit pricing formula that depends on knowledge of a characteristic…

We study stochastic model reduction for evolution equations in infinite dimensional Hilbert spaces, and show the convergence to the reduced equations via abstract results of Wong-Zakai type for stochastic equations driven by a scaled…

We study the estimation of leverage effect and volatility of volatility by using high-frequency data with the presence of jumps. We first construct spot volatility estimator by using the empirical characteristic function of the…

Local Stochastic Volatility (LSV) models have been used for pricing and hedging derivatives positions for over twenty years. An enormous body of literature covers analytical and numerical techniques for calibrating the model to market data.…

We consider two kinds of stochastic volatility models. Both kinds of models contain a stationary volatility process, the density of which, at a fixed instant in time, we aim to estimate. We discuss discrete time models where for instance a…

First the relation between shift selfsimilar additive sequences and stationary sequences of Ornstein-Uhlenbeck type (OU type) on $\mathbb{R}^d$ is shown and then the rates of escape for shift selfsimilar additive sequences are discussed. As…

Lognormality was found experimentally for coarse-grained squared turbulence velocity and velocity increment when the coarsening scale is comparable to the correlation scale of the velocity (Mouri et al. Phys. Fluids 21, 065107, 2009). We…

In this paper, we focus on the problem of optimal portfolio-consumption policies in a multi-asset financial market, where the n risky assets follow Exponential Ornstein-Uhlenbeck processes, along with one risk-free bond. The investor's…

An Ornstein-Uhlenbeck (OU) process can be considered as a continuous time interpolation of the discrete time AR$(1)$ process. Departing from this fact, we analyse in this work the effect of iterating OU treated as a linear operator that…

In this paper, we study stochastic volatility models in regimes where the maturity is small, but large compared to the mean-reversion time of the stochastic volatility factor. The problem falls in the class of averaging/homogenization…

A Levy-driven Ornstein-Uhlenbeck process is proposed to model the evolution of the risk-free rate and default intensities for the purpose of evaluating option contracts on a credit index. Time evolution in credit markets is assumed to…

In this paper, we establish sample path large and moderate deviation principles for log-price processes in Gaussian stochastic volatility models, and study the asymptotic behavior of exit probabilities, call pricing functions, and the…

Based on a criterion of mathematical simplicity and consistency with empirical market data, a stochastic volatility model has been obtained with the volatility process driven by fractional noise. Depending on whether the stochasticity…

In financial markets, low prices are generally associated with high volatilities and vice-versa, this well known stylized fact usually being referred to as leverage effect. We propose a local volatility model, given by a stochastic…

The article is devoted to models of financial markets with stochastic volatility, which is defined by a functional of Ornstein-Uhlenbeck process or Cox-Ingersoll-Ross process. We study the question of exact price of European option. The…

Empirical studies show that the volatility may exhibit correlations that decay as a fractional power of the time offset. The paper presents a rigorous analysis for the case when the stationary stochastic volatility model is constructed in…

This paper presents a study using the Bayesian approach in stochastic volatility models for modeling financial time series, using Hamiltonian Monte Carlo methods (HMC). We propose the use of other distributions for the errors in the…

We show that typical behaviors of market participants at the high frequency scale generate leverage effect and rough volatility. To do so, we build a simple microscopic model for the price of an asset based on Hawkes processes. We encode in…