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We introduce a novel simulation scheme, iVi (integrated Volterra implicit), for integrated Volterra square-root processes and Volterra Heston models based on the Inverse Gaussian distribution. The scheme is designed to handle $L^1$ kernels…
The lifted Heston model is a stochastic volatility model emerging as a Markovian lift of the rough Heston model and the class of rough volatility processes. The model encodes the path dependency of volatility on a set of N square-root state…
We simultaneously estimate the four parameters of a subcritical Heston process. We do not restrict ourself to the case where the stochastic volatility process never reaches zero. In order to avoid the use of unmanageable stopping times and…
Efficient sampling for the conditional time integrated variance process in the Heston stochastic volatility model is key to the simulation of the stock price based on its exact distribution. We construct a new series expansion for this…
We provide an efficient and accurate simulation scheme for the rough Heston model in the standard ($H>0$) as well as the hyper-rough regime ($H > -1/2$). The scheme is based on low-dimensional Markovian approximations of the rough Heston…
Recent years have seen an increased level of interest in pricing equity options under a stochastic volatility model such as the Heston model. Often, simulating a Heston model is difficult, as a standard finite difference scheme may lead to…
Consider a process, stochastic or deterministic, obtained by using a numerical integration scheme, or from Monte-Carlo methods involving an approximation to an integral, or a Newton-Raphson iteration to approximate the root of an equation.…
This paper provides an algorithm for simulating improper (or noncircular) complex-valued stationary Gaussian processes. The technique utilizes recently developed methods for multivariate Gaussian processes from the circulant embedding…
Brown-Resnick processes are max-stable processes that are associated to Gaussian processes. Their simulation is often based on the corresponding spectral representation which is not unique. We study to what extent simulation accuracy and…
This paper presents a new numerical scheme for simulating stochastic processes specified by their marginal distribution functions and covariance functions. Stochastic samples are firstly generated to automatically satisfy target marginal…
Matrix square roots and their inverses arise frequently in machine learning, e.g., when sampling from high-dimensional Gaussians $\mathcal{N}(\mathbf 0, \mathbf K)$ or whitening a vector $\mathbf b$ against covariance matrix $\mathbf K$.…
We introduce a novel and efficient simulation scheme for Hawkes processes on a fixed time grid, leveraging their affine Volterra structure. The key idea is to first simulate the integrated intensity and the counting process using Inverse…
The transition probability of a Cox-Ingersoll-Ross process can be represented by a non-central chi-square density. First we prove a new representation for the central chi-square density based on sums of powers of generalized Gaussian random…
Nested simulation concerns estimating functionals of a conditional expectation via simulation. In this paper, we propose a new method based on kernel ridge regression to exploit the smoothness of the conditional expectation as a function of…
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…
Exact simulation schemes under the Heston stochastic volatility model (e.g., Broadie-Kaya and Glasserman-Kim) suffer from computationally expensive modified Bessel function evaluations. We propose a new exact simulation scheme without the…
In this article, we introduce parallel-in-time methods for state and parameter estimation in general nonlinear non-Gaussian state-space models using the statistical linear regression and the iterated statistical posterior linearization…
We propose a randomised version of the Heston model-a widely used stochastic volatility model in mathematical finance-assuming that the starting point of the variance process is a random variable. In such a system, we study the small-and…
In this paper we derive a new direct inversion method to simulate squared Bessel processes. Since the transition probability of these processes can be represented by a non-central chi-square distribution, we construct an efficient and…
This paper proposes a novel multiscale estimator for the integrated volatility of an Ito process, in the presence of market microstructure noise (observation error). The multiscale structure of the observed process is represented…