Related papers: Discretizing the Heston Model: An Analysis of the …

Score-based diffusion models have emerged as powerful tools in generative modeling, yet their theoretical foundations remain underexplored. In this work, we focus on the Wasserstein convergence analysis of score-based diffusion models.…

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…

We introduce a general framework allowing to apply the theory of regularity structures to discretisations of stochastic PDEs. The approach pursued in this article is that we do not focus on any one specific discretisation procedure.…

A general method to construct recombinant tree approximations for stochastic volatility models is developed and applied to the Heston model for stock price dynamics. In this application, the resulting approximation is a four tuple Markov…

Sharp asymptotic lower bounds of the expected quadratic variation of discretization error in stochastic integration are given. The theory relies on inequalities for the kurtosis and skewness of a general random variable which are themselves…

In quantitative finance, modeling the volatility structure of underlying assets is vital to pricing options. Rough stochastic volatility models, such as the rough Bergomi model [Bayer, Friz, Gatheral, Quantitative Finance 16(6), 887-904,…

Higher-order regularization problem formulations are popular frameworks used in machine learning, inverse problems and image/signal processing. In this paper, we consider the computational problem of finding the minimizer of the Sobolev…

We introduce a novel multi-factor Heston-based stochastic volatility model, which is able to reproduce consistently typical multi-dimensional FX vanilla markets, while retaining the (semi)-analytical tractability typical of affine models…

This paper deals with the intersection point process of a stationary and isotropic Poisson hyperplane process in $\mathbb{R}^d$ of intensity $t>0$, where only hyperplanes that intersect a centred ball of radius $R>0$ are considered. Taking…

We introduce a novel stochastic volatility model where the squared volatility of the asset return follows a Jacobi process. It contains the Heston model as a limit case. We show that the joint density of any finite sequence of log returns…

In this paper, we consider the problem of pricing discretely-sampled variance swaps based on a hybrid model of stochastic volatility and stochastic interest rate with regime-switching. Our modelling framework extends the Heston stochastic…

We consider hedging of a contingent claim by a 'semi-static' strategy composed of a dynamic position in one asset and static (buy-and-hold) positions in other assets. We give general representations of the optimal strategy and the hedging…

The main purpose of the paper is to derive Thiele's differential equation for unit-linked policies in the Heston-Hawkes stochastic volatility model introduced in arXiv:2210.15343. This model is an extension of the well-known Heston model…

This paper considers the case of pricing discretely-sampled variance swaps under the class of equity-interest rate hybridization. Our modeling framework consists of the equity which follows the dynamics of the Heston stochastic volatility…

In this paper, we employ the Heston stochastic volatility model to describe the stock's volatility and apply the model to derive and analyze the optimal trading strategies for dealers in a security market. We also extend our study to option…

We study large deviation properties of systems of weakly interacting particles modeled by It\^{o} stochastic differential equations (SDEs). It is known under certain conditions that the corresponding sequence of empirical measures…

Deep hedging trains neural networks to manage derivative risk under market frictions, but produces hedge ratios with no measure of model confidence -- a significant barrier to deployment. We introduce uncertainty quantification to the deep…

In this paper we present a novel approach towards variance reduction for discretised diffusion processes. The proposed approach involves specially constructed control variates and allows for a significant reduction in the variance for the…

Tensor regression is an important tool for tensor data analysis, but existing works have not considered the impact of outliers, making them potentially sensitive to such data points. This paper proposes a low tubal rank robust regression…

A recent paper [J. A. Evans, D. Kamensky, Y. Bazilevs, "Variational multiscale modeling with discretely divergence-free subscales", Computers & Mathematics with Applications, 80 (2020) 2517-2537] introduced a novel stabilized finite element…