Related papers: Short-time asymptotics for non self-similar stocha…
We establish a comprehensive sample path large deviation principle (LDP) for log-processes associated with multivariate time-inhomogeneous stochastic volatility models. Examples of models for which the new LDP holds include Gaussian models,…
We study fractional stochastic volatility models in which the volatility process is a positive continuous function $\sigma$ of a continuous Gaussian process $\widehat{B}$. Forde and Zhang established a large deviation principle for the…
We study multidimensional stochastic volatility models in which the volatility process is a positive continuous function of a continuous multidimensional Volterra process that can be not self-similar. The main results obtained in this paper…
Using the large deviation principle (LDP) for a re-scaled fractional Brownian motion $B^H_t$ where the rate function is defined via the reproducing kernel Hilbert space, we compute small-time asymptotics for a correlated fractional…
We develop a variant of rough path theory tailor-made for analyzing a class of financial asset price models known as rough volatility models. As an application, we prove a pathwise large deviation principle (LDP) for a certain class of…
We introduce time-inhomogeneous stochastic volatility models, in which the volatility is described by a nonnegative function of a Volterra type continuous Gaussian process that may have very rough sample paths. The main results obtained in…
In this paper, we prove the large deviation principle (LDP) for stochastic differential equations driven by stochastic integrals in one dimension. The result can be proved with a minimal use of rough path theory, and this implies the LDP…
We consider the short time behaviour of stochastic systems affected by a stochastic volatility evolving at a faster time scale. We study the asymptotics of a logarithmic functional of the process by methods of the theory of homogenisation…
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…
We introduce stochastic volatility models, in which the volatility is described by a time-dependent nonnegative function of a reflecting diffusion. The idea to use reflecting diffusions as building blocks of the volatility came into being…
Rough volatility models are continuous time stochastic volatility models where the volatility process is driven by a fractional Brownian motion with the Hurst parameter smaller than half, and have attracted much attention since a seminal…
It has been recently shown that spot volatilities can be very well modeled by rough stochastic volatility type dynamics. In such models, the log-volatility follows a fractional Brownian motion with Hurst parameter smaller than 1/2. This…
The research presented in this article provides an alternative option pricing approach for a class of rough fractional stochastic volatility models. These models are increasingly popular between academics and practitioners due to their…
We study stochastic volatility models in which the volatility process is a positive continuous function of a continuous Volterra stochastic process. We state some pathwise large deviation principles for the scaled log-price.
We consider rough stochastic volatility models where the variance process satisfies a stochastic Volterra equation with the fractional kernel, as in the rough Bergomi and the rough Heston model. In particular, the variance process is…
We study Euler-type discrete-time schemes for the rough Heston model, which can be described by a stochastic Volterra equation (with non-Lipschtiz coefficient functions), or by an equivalent integrated variance formulation. Using weak…
We derive the short-maturity asymptotics for prices of options on realized variance in local-stochastic volatility models. We consider separately the short-maturity asymptotics for out-of-the-money and in-the-money options cases. The…
We study stochastic volatility models in which the volatility process is a function of a continuous fractional stochastic process, which is an integral transform of the solution of an SDE satisfying the Yamada-Watanabe condition. We…
Predicting the conditional evolution of Volterra processes with stochastic volatility is a crucial challenge in mathematical finance. While deep neural network models offer promise in approximating the conditional law of such processes,…
To investigate the complex dynamics of a biological neuron that is subject to small random perturbations we can use stochastic neuron models. While many techniques have already been developed to study properties of such models, especially…