Related papers: Monte-Carlo Option Pricing in Quantum Parallel
We introduce two kinds of quantum algorithms to explore microcanonical and canonical properties of many-body systems. The first one is a hybrid quantum algorithm that, given an efficiently preparable state, computes expectation values in a…
The complexity is increasing rapidly in many areas of the automotive industry. The design of an automobile involves many different engineering disciplines, e. g., mechanical, electrical, and software engineering. The software of a vehicle…
Quantum amplitude amplification and estimation have shown quadratic speedups to unstructured search and estimation tasks. We show that a coherent combination of these quantum algorithms also provides a quadratic speedup to calculating the…
We consider the problem of pricing discretely monitored Asian options over $T$ monitoring points where the underlying asset is modeled by a geometric Brownian motion. We provide two quantum algorithms with complexity poly-logarithmic in $T$…
We propose quantum algorithms that provide provable speedups for Markov Chain Monte Carlo (MCMC) methods commonly used for sampling from probability distributions of the form $\pi \propto e^{-f}$, where $f$ is a potential function. Our…
Classical optimization is a cornerstone of the success of variational quantum algorithms, which often require determining the derivatives of the cost function relative to variational parameters. The computation of the cost function and its…
Pricing options is an important problem in financial engineering. In many scenarios of practical interest, financial option prices associated to an underlying asset reduces to computing an expectation w.r.t.~a diffusion process. In general,…
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)…
Monte Carlo integration approximates an integral of a black-box function by taking the average of many evaluations (i.e., samples) of the function (integrand). For $N$ queries of the integrand, Monte Carlo integration achieves the…
Optimization problems are prevalent in various fields, and the gradient-based gradient descent algorithm is a widely adopted optimization method. However, in classical computing, computing the numerical gradient for a function with $d$…
Using tools from spectral analysis, singular and regular perturbation theory, we develop a systematic method for analytically computing the approximate price of a derivative-asset. The payoff of the derivative-asset may be path-dependent.…
We develop the idea of using Monte Carlo sampling of random portfolios to solve portfolio investment problems. In this first paper we explore the need for more general optimization tools, and consider the means by which constrained random…
The main idea of this work is that the quantum-classical isomorphism is a suitable framework for a generalization of the notion of detailed balance. The quantum-classical isomorphism is used in order to develop a Monte Carlo simulation with…
Stochastic processes play a fundamental role in physics, mathematics, engineering and finance. One potential application of quantum computation is to better approximate properties of stochastic processes. For example, quantum algorithms for…
It is known that quantum computers can speed up Monte Carlo simulation compared to classical counterparts. There are already some proposals of application of the quantum algorithm to practical problems, including quantitative finance. In…
A simple and efficient method for quantum Monte Carlo simulation is presented, based on discretization of the action in the path integral, and a Gaussian averaging of the potential, which works well e.g. with the Coulomb potential.
Efficiently pricing multi-asset options is a challenging problem in quantitative finance. When the characteristic function is available, Fourier-based methods are competitive compared to alternative techniques because the integrand in the…
Monte Carlo is a simple and flexible tool that is widely used in computational finance. In this context, it is common for the quantity of interest to be the expected value of a random variable defined via a stochastic differential equation.…
Classical optimization algorithms in machine learning often take a long time to compute when applied to a multi-dimensional problem and require a huge amount of CPU and GPU resource. Quantum parallelism has a potential to speed up machine…
Combining quantum computers with classical compute power has become a standard means for developing algorithms that are eventually supposed to beat any purely classical alternatives. While in-principle advantages for solution quality or…