Related papers: Saddle-Point Approach to Large-Time Volatility Smi…
This paper develops a Bayesian procedure for estimation and forecasting of the volatility of multivariate time series. The foundation of this work is the matrix-variate dynamic linear model, for the volatility of which we adopt a…
Many economic variables feature changes in their conditional mean and volatility, and Time Varying Vector Autoregressive Models are often used to handle such complexity in the data. Unfortunately, when the number of series grows, they…
We demonstrate the large deviation principle in the small noise limit for the mild solution of stochastic evolution equations with monotone nonlinearity. A recently developed method, weak convergent method, has been employed in studying the…
Stable distribution is one of the attractive models that well describes fat-tail behaviors and scaling phenomena in various scientific fields. The approach based upon the method of moments yields a simple procedure for estimating stable law…
We study the exponential Ornstein-Uhlenbeck stochastic volatility model and observe that the model shows a multiscale behavior in the volatility autocorrelation. It also exhibits a leverage correlation and a probability profile for the…
Stochastic volatility (SV) models are nonlinear state-space models that enjoy increasing popularity for fitting and predicting heteroskedastic time series. However, due to the large number of latent quantities, their efficient estimation is…
We consider stochastic control systems affected by a fast mean reverting volatility $Y(t)$ driven by a pure jump L\'evy process. Motivated by a large literature on financial models, we assume that $Y(t)$ evolves at a faster time scale…
Agents' heterogeneity is recognized as a driver mechanism for the persistence of financial volatility. We focus on the multiplicity of investment strategies' horizons, we embed this concept in a continuous time stochastic volatility…
For a general class of saddle point problems sharp estimates for Babu\v{s}ka's inf-sup stability constants are derived in terms of the constants in Brezzi's theory. In the finite-dimensional Hermitian case more detailed spectral properties…
We propose Variational Heteroscedastic Volatility Model (VHVM) -- an end-to-end neural network architecture capable of modelling heteroscedastic behaviour in multivariate financial time series. VHVM leverages recent advances in several…
We present a general class of spatio-temporal stochastic processes describing the causal evolution of a positive-valued field in space and time. The field construction is based on independently scattered random measures of Levy type whose…
How does a steady state with strong intermittency develop in time from an initial state which is statistically random? For passive sliders driven by various fluctuating surfaces, we show that the approach involves an indefinitely growing…
Our derivation of the distribution function for future returns is based on the risk neutral approach which gives a functional dependence for the European call (put) option price, C(K), given the strike price, K, and the distribution…
We introduce a class of randomly time-changed fast mean-reverting stochastic volatility models and, using spectral theory and singular perturbation techniques, we derive an approximation for the prices of European options in this setting.…
This paper introduces a Bayesian vector autoregression (BVAR) with stochastic volatility-in-mean and time-varying skewness. Unlike previous approaches, the proposed model allows both volatility and skewness to directly affect macroeconomic…
This paper introduces a continuous-time stochastic dynamical framework for understanding how large language models (LLMs) may self-amplify latent biases or toxicity through their own chain-of-thought reasoning. The model posits an…
Stochastic process models for spatiotemporal data underlying random fields find substantial utility in a range of scientific disciplines. Subsequent to predictive inference on the values of the random field (or spatial surface indexed…
It is known that Heston's stochastic volatility model exhibits moment explosion, and that the critical moment $s_+$ can be obtained by solving (numerically) a simple equation. This yields a leading order expansion for the implied volatility…
Long-time-integrated quantities in stochastic processes, in or out of equilibrium, usually exhibit rare but huge fluctuations. Work or heat production is such a quantity, of which the probability distribution function displays an…
The article is devoted to the development of numerical methods for solving saddle point problems and variational inequalities with simplified requirements for the smoothness conditions of functionals. Recently there were proposed some…