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This paper explores the application of Machine Learning techniques for pricing high-dimensional options within the framework of the Uncertain Volatility Model (UVM). The UVM is a robust framework that accounts for the inherent…
In this paper, we investigate reflected backward stochastic differential equations driven by rough paths (rough RBSDEs), which can be viewed as probabilistic representations of nonlinear rough partial differential equations (rough PDEs) or…
We investigate the performance of the Deep Hedging framework under training paths beyond the (finite dimensional) Markovian setup. In particular we analyse the hedging performance of the original architecture under rough volatility models…
Cryptocurrency markets are characterized by extreme volatility, making accurate forecasts essential for effective risk management and informed trading strategies. Traditional deterministic (point) forecasting methods are inadequate for…
Learning the parameters of a (potentially partially observable) random field model is intractable in general. Instead of focussing on a single optimal parameter value we propose to treat parameters as dynamical quantities. We introduce an…
This paper presents the exact mathematical derivation of the mean and variance properties for the Exponentially Weighted Moving Average (EWMA) statistic applied to binomial proportion monitoring in Multiple Stream Processes (MSPs). We…
Diffusion processes driven by Fractional Brownian motion (FBM) have often been considered in modeling stock price dynamics in order to capture the long range dependence of stock price observed in reality. Option prices for such models had…
We present an empirical study examining several claims related to option prices in rough volatility literature using SPX options data. Our results show that rough volatility models with the parameter $H \in (0,1/2)$ are inconsistent with…
We perform an extensive empirical analysis of scaling properties of equity returns, suggesting that financial data show time varying multifractal properties. This is obtained by comparing empirical observations of the weighted generalised…
We develop a nonparametric test for deciding whether volatility of an asset follows a standard semimartingale process, with paths of finite quadratic variation, or a rough process with paths of infinite quadratic variation. The test…
Parametric estimation of stochastic differential equations (SDEs) has been a subject of intense studies already for several decades. The Heston model for instance is driven by two coupled SDEs and is often used in financial mathematics for…
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…
In this paper, we consider a complex-valued d-dimensional fractional Brownian motion defined on the closure of the complex upper half-plane, called analytic fractional Brownian motion. This process has been introduced by the second author…
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…
This study investigates the efficacy of Conditional Restricted Boltzmann Machines (CRBMs) for modeling high-dimensional financial time series and detecting systemic risk regimes. We extend the classical application of static Restricted…
This work develops change-point methods for statistics of high-frequency data. The main interest is in the volatility of an It\^{o} semi-martingale, the latter being discretely observed over a fixed time horizon. We construct a…
Computational Fluid Dynamics (CFD) simulations using turbulence models are commonly used in engineering design. Of the different turbulence modeling approaches that are available, eddy viscosity based models are the most common for their…
The dynamic hedging theory only makes sense in the setup of one given model, whereas the practice of dynamic hedging is just the opposite, with models fleeing after the data through daily recalibration. This is quite of a quantitative…
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)…
The Heston stochastic volatility model is a standard model for valuing financial derivatives, since it can be calibrated using semi-analytical formulas and captures the most basic structure of the market for financial derivatives with…