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Building on a prominent agent-based model, we present a new structural stochastic volatility asset pricing model of fundamentalists vs. chartists where the prices are determined based on excess demand. Specifically, this allows for…
In [Precise Asymptotics for Robust Stochastic Volatility Models; Ann. Appl. Probab. 2021] we introduce a new methodology to analyze large classes of (classical and rough) stochastic volatility models, with special regard to short-time and…
In the setting of stochastic Volterra equations, and in particular rough volatility models, we show that conditional expectations are the unique classical solutions to path-dependent PDEs. The latter arise from the functional It\^o formula…
In Gatheral et al. 2018, first posted in 2014, volatility is characterized by fractional behavior with a Hurst exponent $H < 0.5$, challenging traditional views of volatility dynamics. Gatheral et al. demonstrated this using realized…
We present a discrete time stochastic volatility model in which the conditional distribution of the logreturns is a Variance-Gamma, that is a normal variance-mean mixture with Gamma mixing density. We assume that the Gamma mixing density is…
Semi-lagrangian schemes for discretization of the dynamic programming principle are based on a time discretization projected on a state-space grid. The use of a structured grid makes this approach not feasible for high-dimensional problems…
Diffusion models have emerged as powerful tools for generative modeling, demonstrating exceptional capability in capturing target data distributions from large datasets. However, fine-tuning these massive models for specific downstream…
We develop an arbitrage-free deep learning framework for yield curve and bond price forecasting based on the Heath-Jarrow-Morton (HJM) term-structure model and a dynamic Nelson-Siegel parameterization of forward rates. Our approach embeds a…
Implied volatility is at the very core of modern finance, notwithstanding standard option pricing models continue to derive option prices starting from the joint dynamics of the underlying asset price and the spot volatility. These models…
This paper develops a flexible and computationally efficient multivariate volatility model, which allows for dynamic conditional correlations and volatility spillover effects among financial assets. The new model has desirable properties…
We consider a variance reduction approach for the stochastic homogenization of divergence form linear elliptic problems. Although the exact homogenized coefficients are deterministic, their practical approximations are random. We introduce…
A novel random field model or the reconstruction of turbulent velocity fluctuations from inhomogeneous characteristic flow quantities in terms of stochastic Fourier-type integrals has recently been introduced and analyzed by the authors.…
Volatility modelling has become a significant area of research within Financial Mathematics. Wiener process driven stochastic volatility models have become popular due their consistency with theoretical arguments and empirical observations.…
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 construct a statistical indicator for the detection of short-term asset price bubbles based on the information content of bid and ask market quotes for plain vanilla put and call options. Our construction makes use of the martingale…
This paper introduces unified models for high-dimensional factor-based Ito process, which can accommodate both continuous-time Ito diffusion and discrete-time stochastic volatility (SV) models by embedding the discrete SV model in the…
There is growing interest in a hybrid control design for treatment evaluation, where a randomized controlled trial is augmented with external control data from a previous trial or a real world data source. The hybrid control design has the…
The Fractional Stochastic Regularity Model (FSRM) is an extension of Black-Scholes model describing the multifractal nature of prices. It is based on a multifractional process with a random Hurst exponent $H_t$, driven by a fractional…
This paper addresses the robust ${\cal H}_2$ synthesis problem for linear fractional transformation (LFT) systems subject to structured uncertainty (parameter) and white-noise disturbances. By introducing an intermediate matrix variable, we…
Local Volatility (LV) is a powerful tool for market modeling, enabling the generation of arbitrage-free scenarios calibrated to all European options. To implement LV, we need to interpolate and extrapolate option prices. This approach is…