Related papers: Quasi-Monte Carlo methods for the Heston model
This paper presents an algorithm for a complete and efficient calibration of the Heston stochastic volatility model. We express the calibration as a nonlinear least squares problem. We exploit a suitable representation of the Heston…
We combine the one-dimensional Monte Carlo simulation and the semi-analytical one-dimensional heat potential method to design an efficient technique for pricing barrier options on assets with correlated stochastic volatility. Our approach…
The use of sequential Monte Carlo within simulation for path-dependent option pricing is proposed and evaluated. Recently, it was shown that explicit solutions and importance sampling are valuable for efficient simulation of spot price and…
In this paper we propose and analyse a method for estimating three quantities related to an Asian option: the fair price, the cumulative distribution function, and the probability density. The method involves preintegration with respect to…
Local volatility models usually capture the surface of implied volatilities more accurately than other approaches, such as stochastic volatility models. We present the results of application of Monte Carlo (MC) and Quasi Monte Carlo (QMC)…
This article provides a high-level overview of some recent works on the application of quasi-Monte Carlo (QMC) methods to PDEs with random coefficients. It is based on an in-depth survey of a similar title by the same authors, with an…
Quasi-Monte Carlo methods have become the industry standard in computer graphics. For that purpose, efficient algorithms for low discrepancy sequences are discussed. In addition, numerical pitfalls encountered in practice are revealed. We…
This paper introduces a class of Monte Carlo algorithms which are based upon the simulation of a Markov process whose quasi-stationary distribution coincides with a distribution of interest. This differs fundamentally from, say, current…
Though quasi-Newton methods have been extensively studied in the literature, they either suffer from local convergence or use a series of line searches for global convergence which is not acceptable in the distributed setting. In this work,…
We provide a numerically robust and fast method capable of exploiting the local geometry when solving large-scale stochastic optimisation problems. Our key innovation is an auxiliary variable construction coupled with an inverse Hessian…
Machine learning (ML) problems are often posed as highly nonlinear and nonconvex unconstrained optimization problems. Methods for solving ML problems based on stochastic gradient descent are easily scaled for very large problems but may…
We have developed an efficient Monte Carlo algorithm, which accelerates slow Monte Carlo dynamics in quasi-one-dimensional Ising spin systems. The loop algorithm of the quantum Monte Carlo method is applied to the classical spin models with…
Exact path simulation of the underlying state variable is of great practical importance in simulating prices of financial derivatives or their sensitivities when there are no analytical solutions for their pricing formulas. However, in…
We propose a communication efficient quasi-Newton method for large-scale multi-agent convex composite optimization. We assume the setting of a network of agents that cooperatively solve a global minimization problem with strongly convex…
Quasi-Monte Carlo (QMC) methods for estimating integrals are attractive since the resulting estimators typically converge at a faster rate than pseudo-random Monte Carlo. However, they can be difficult to set up on arbitrary posterior…
This paper presents a methodology to introduce time-dependent parameters for a wide family of models preserving their analytic tractability. This family includes hybrid models with stochastic volatility, stochastic interest-rates, jumps and…
This project investigates the applicability of quasi-Monte Carlo methods to Euclidean lattice systems in order to improve the asymptotic error scaling of observables for such theories. The error of an observable calculated by averaging over…
Adaptive protocols enable the construction of more efficient state preparation circuits in variational quantum algorithms (VQAs) by utilizing data obtained from the quantum processor during the execution of the algorithm. This idea…
We propose the quasi-Monte Carlo method for linear combination of unitaries via classical post-processing (LCU-CPP) on quantum applications. The LCU-CPP framework has been proposed as an approach to reduce hardware resources, expressing a…
We present a universal quantum Monte Carlo algorithm for simulating arbitrary high-spin (spin greater than 1/2) Hamiltonians, based on the recently developed permutation matrix representation (PMR) framework. Our approach extends a…