Related papers: Quantum Monte Carlo algorithm for option pricing a…
Quantum computing and quantum Monte Carlo (QMC) are respectively the state-of-the-art quantum and classical computing methods for understanding many-body quantum systems. Here, we propose a hybrid quantum-classical algorithm that integrates…
This paper develops three polynomial-time pricing techniques for European Asian options with provably small errors, where the stock prices follow binomial trees or trees of higher-degree. The first technique is the first known Monte Carlo…
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…
In this article we consider the problem of pricing and hedging high-dimensional Asian basket options by Quasi-Monte Carlo simulation. We assume a Black-Scholes market with time-dependent volatilities and show how to compute the deltas by…
Monte Carlo sampling is a powerful toolbox of algorithmic techniques widely used for a number of applications wherein some noisy quantity, or summary statistic thereof, is sought to be estimated. In this paper, we survey the literature for…
Several quantum and classical Monte Carlo algorithms for Betti Number Estimation (BNE) on clique complexes have recently been proposed, though it is unclear how their performances compare. We review these algorithms, emphasising their…
Pricing exotic multi-asset path-dependent options requires extensive Monte Carlo simulations. In the recent years the interest to the Quasi-monte Carlo technique has been renewed and several results have been proposed in order to improve…
We apply a physics-informed deep-learning approach the PINN approach to the Black-Scholes equation for pricing American and European options. We test our approach on both simulated as well as real market data, compare it to…
In this Article, a fast numerical numerical algorithm for pricing discrete double barrier option is presented. According to Black-Scholes model, the price of option in each monitoring date can be evaluated by a recursive formula upon the…
We apply multilevel Monte Carlo for option pricing problems using exponential L\'{e}vy models with a uniform timestep discretisation to monitor the running maximum required for lookback and barrier options. The numerical results demonstrate…
Recent studies have demonstrated the efficiency of Variational Autoencoders (VAE) to compress high-dimensional implied volatility surfaces into a low dimensional representation. Although this method can be effectively used for pricing…
In recent years, tremendous progress has been made on numerical algorithms for solving partial differential equations (PDEs) in a very high dimension, using ideas from either nonlinear (multilevel) Monte Carlo or deep learning. They are…
G-expectation, as a sublinear expectation, provides a powerful framework for modeling uncertainty in financial markets. Motivated by the need for robust valuation under model uncertainty, this work develops a unified risk-neutral valuation…
It is known that quantum computers yield a speed-up for certain discrete problems. Here we want to know whether quantum computers are useful for continuous problems. We study the computation of the integral of functions from the classical…
Collateralized debt obligation (CDO) has been one of the most commonly used structured financial products and is intensively studied in quantitative finance. By setting the asset pool into different tranches, it effectively works out and…
This Perspective focuses on the several overlaps between quantum algorithms and Monte Carlo methods in the domains of physics and chemistry. We will analyze the challenges and possibilities of integrating established quantum Monte Carlo…
We extend a recently developed method to solve semi-linear PDEs to the case of a degenerated diffusion. Being a pure Monte Carlo method it does not suffer from the so called curse of dimensionality and it can be used to solve problems that…
This tutorial paper introduces quantum approaches to Monte Carlo computation with applications in computational finance. We outline the basics of quantum computing using Grover's algorithm for unstructured search to build intuition. We then…
Standard quantum amplitude estimation algorithms provide quadratic speedup to Monte-Carlo simulations but require a circuit depth that scales as inverse of the estimation error. In view of the shallow depth in near-term devices, the…
The Variational Monte Carlo method has recently seen important advances through the use of neural network quantum states. While more and more sophisticated ans\"atze have been designed to tackle a wide variety of quantum many-body problems,…