Related papers: Rough SABR Forward Market Model
We present a number of related comparison results, which allow to compare moment explosion times, moment generating functions and critical moments between rough and non-rough Heston models of stochastic volatility. All results are based on…
For option pricing models and heavy-tailed distributions, this study proposes a continuous-time stochastic volatility model based on an arithmetic Brownian motion: a one-parameter extension of the normal stochastic alpha-beta-rho (SABR)…
This study presents contemporaneous modeling of asset return and price range within the framework of stochastic volatility with leverage. A new representation of the probability density function for the price range is provided, and its…
The scope of this manuscript is to review some recent developments in statistics for discretely observed semimartingales which are motivated by applications for financial markets. Our journey through this area stops to take closer looks at…
The analysis of high-frequency financial data is often impeded by the presence of noise. This article is motivated by intraday return data in which market microstructure noise appears to be rough, that is, best captured by a continuous-time…
Non-stationary extremal dependence, whereby the relationship between the extremes of multiple variables evolves over time, is commonly observed in many environmental and financial data sets. However, most multivariate extreme value models…
In this work we introduce Heath-Jarrow-Morton (HJM) interest rate models driven by fractional Brownian motions. By using support arguments we prove that the resulting model is arbitrage free under proportional transaction costs in the same…
Regime-switching models, in particular Hidden Markov Models (HMMs) where the switching is driven by an unobservable Markov chain, are widely-used in financial applications, due to their tractability and good econometric properties. In this…
Volatility prediction for financial assets is one of the essential questions for understanding financial risks and quadratic price variation. However, although many novel deep learning models were recently proposed, they still have a "hard…
It is well known that the Cox-Ingersoll-Ross (CIR) stochastic model to study the term structure of interest rates, as introduced in 1985, is inadequate for modelling the current market environment with negative short interest rates.…
We consider the Heath-Jarrow-Morton model of forward rates processes with linear volatility. The noise is either a Wiener or a pure jump Leevy process. We provide formulae for the forward rate processes, and discus the problem of their…
We propose a new flexible tensor model for multiple-equation regression that accounts for latent regime changes. The model allows for dynamic coefficients and multi-dimensional covariates that vary across equations. We assume the…
The Gaussian Graphical Model (GGM) is a popular tool for incorporating sparsity into joint multivariate distributions. The G-Wishart distribution, a conjugate prior for precision matrices satisfying general GGM constraints, has now been in…
We propose to take advantage of the common knowledge of the characteristic function of the swap rate process as modelled in the LIBOR Market Model with Stochastic Volatility and Displaced Diffusion (DDSVLMM) to derive analytical expressions…
In this non-technical introduction to diamond trees and forests, we focus on their application to computation in stochastic volatility models written in forward variance form, rough volatility models in particular.
We propose a heterogeneous simultaneous graphical dynamic linear model (H-SGDLM), which extends the standard SGDLM framework to incorporate a heterogeneous autoregressive realised volatility (HAR-RV) model. This novel approach creates a…
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 forward-backward representation (FB) is a recently proposed framework (Touati et al., 2023; Touati & Ollivier, 2021) to train behavior foundation models (BFMs) that aim at providing zero-shot efficient policies for any new task…
The rough Bergomi (rBergomi) model can accurately describe the historical and implied volatilities, and has gained much attention in the past few years. However, there are many hidden unknown parameters or even functions in the model. In…
Continuous time financial market models are often motivated as scaling limits of discrete time models. The objective of this paper is to establish such a connection for a robust framework. More specifically, we consider discrete time models…