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Monte Carlo Quantum Methods for FinTech

Introduction: Monte Carlo classic methods are related to testing an outcome over a range of possible variables.

The classic simulations based on classic Monte Carlo methods are used to test the outcomes on a wide combination of possible market returns in trading and investment solutions.

The simulation platform consists of a random number generator which generates a set of numbers from a uniform distribution.

The Monte Carlo classical methods evaluate integrals such as the expected value of a random variable by generating a set of random numbers and average.

Quantum walks are a quantum analogue to random walks and have substantially reduced the time-consumption in Monte Carlo simulations for mixing of Markov chains.

Monte Carlo Quantum methods are used for options pricing, evaluating hedge strategies, return predictions, portfolio evaluation, personal financial planning and capital investment impact.

Monte Carlo based methods answer how to estimate the risk and return of a portfolio based on stocks, bonds, options and futures.

The risk is measured based on the distribution of returns and the degree of variation of a trading price series over time.

Quantum Monte Carlo simulations are used in retirement planning to predict the likelihood that you will have a particular level of retirement income through life expectancy.

The typical Monte Carlo simulation for retirement involves five variables such as portfolio size, allocation, annual income to be withdrawn, inflation increases to be applied to the income withdrawn and time horizon.

The quantum algorithm for random number generation helps in generating randomness due to the inherent randomness of the quantum state.

This model assumes assets such as risk-free bonds and risky options can be bought and sold continuously in fractional and unlimited quantities without transaction costs.

Several algorithms are developed so far to encompass the need to accelerate the classical deterministic and randomised algorithms with rigorous performance bounds — the error rates of outcome benchmark the effectiveness of these algorithms.

The line of research on performing quantum integration algorithms started from Abrams and Williams (1999), who established the foreground which finally helped in the development of parallel computation of high dimensional integrals by Heinrich et al.

These methods focus on the pricing of financial derivatives and how the arrangement of probability distributions can leverage the advantages of quantum superposition and thus accelerate the simulation.

A typical method uses optimized wave function in diffusion Monte Carlo for accurate and lowest energy calculations.

The finite temperature methods are Auxiliary field, continuous time, determinant quantum, hybrid quantum, path integral and stochastic green function algorithms.

Quantum Monte Carlo algorithms take advantage of parallelism to generate results of high quality and benchmark less expensive methods.

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