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Many of the problems facing the finance community have no known analytical solution. As a result, numerical methods and computer opțiuni binare de combustibil for solving these problems have proliferated.

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This research area is known as computational finance. Many computational finance problems have a high degree of computational complexity and are slow to converge to a solution on classical computers. In particular, when it comes to option pricing, there is additional complexity resulting from the need to respond to quickly changing markets. For example, in order to take advantage of inaccurately priced stock options, the computation must complete before the next change opțiune cuantică the almost continuously changing stock market.

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As a result, the finance community is always looking for ways to overcome the resulting performance issues that arise when pricing options. This has led to research that applies alternative computing techniques to finance. Background on quantum finance[ edit ] One of these alternatives is quantum computing.

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Just as physics models have evolved from classical to quantum, so has computing. Quantum computers have been shown to outperform classical computers when it comes to simulating quantum mechanics [1] as well as for several other algorithms opțiune cuantică as Shor's algorithm for factorization and Grover's algorithm for quantum search, making them an attractive area to research for solving computational finance problems.

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Quantum continuous model[ edit ] Most quantum option pricing research typically focuses on the quantization of the classical Black—Scholes—Merton equation from the perspective of continuous equations opțiune cuantică the Schrödinger equation. Haven builds on the work of Chen and others, [2] but considers the market from the perspective of the Schrödinger equation.

The Schrödinger-based equation that Haven derives has a parameter ħ not to be confused with the complex conjugate of h that represents the amount of arbitrage that is present in the market resulting from a variety of sources including non-infinitely fast price changes, non-infinitely fast information opțiune cuantică and unequal wealth among traders.

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Haven argues that by setting this value appropriately, a more accurate option price can be derived, because in reality, markets are not truly efficient. This is one of the reasons why it is possible that a quantum option pricing opțiune cuantică could be more accurate than a classical one. Baaquie has published many papers on quantum finance and even opțiune cuantică a book that brings many of them together.

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Piotrowski et al. Other models such as Hull—White and Cox—Ingersoll—Ross have successfully used the same approach in the classical setting with interest rate derivatives.

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Accardi and Boukas again quantize the Black—Scholes—Merton equation, but in this case, they also consider the underlying stock to have both Brownian and Poisson processes.

Metaphorically speaking, Chen's quantum opțiune cuantică options pricing model referred opțiune cuantică hereafter as opțiune cuantică quantum binomial model is to existing opțiune cuantică finance models what the Cox—Ross—Rubinstein classical binomial options pricing model was to the Black—Scholes—Merton model: a discretized and simpler version of the same result.

These simplifications make the respective theories not only easier to analyze but also easier to implement on a computer. Multi-step quantum binomial model[ edit ] In the multi-step model the quantum pricing formula is: C.