Quantum options and futures exchange
Quantum options and futures exchange finance is an interdisciplinary research field, applying theories and methods developed by quantum physicists and economists in order to solve problems in finance. It is a branch of econophysics. Finance theory is heavily based on financial instrument pricing such as stock option pricing.
Many of the problems facing the finance community have no known analytical solution. As a result, numerical methods and computer simulations for solving these problems have proliferated. This research area is known as computational finance. Many computational finance problems have a high degree of computational complexity and are slow to quantum options and futures exchange 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 quantum options and futures exchange changing markets.
For example, in order to take advantage of inaccurately priced stock options, the computation must complete before the next change in the almost continuously changing stock market. 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. One of these alternatives is quantum computing. 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  as well as for several other algorithms such 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.
Haven argues that by setting this value appropriately, a more accurate option price can be derived, because in reality, quantum options and futures exchange are not truly efficient. This is one of the reasons why it is possible that a quantum option pricing model could be more accurate than a classical one.
Baaquie  has published many papers on quantum finance and even written a book  that brings many of them together. Core to Baaquie's research and others like Matacz  are Feynman's path integrals. Baaquie applies path integrals to several exotic options and presents analytical results comparing his results to the results of Black—Scholes—Merton equation showing that they are very similar. Instead of assuming it follows a Wiener-Bachelier process,  they assume that quantum options and futures exchange follows an Ornstein-Uhlenbeck process.
Other models such as Hull-White  and Cox-Ingersoll-Ross  have successfully used the same approach quantum options and futures exchange the classical setting with interest rate derivatives. Khrennikov  builds on the work of Haven and quantum options and futures exchange and further bolsters the idea that the market efficiency assumption made by the Black—Scholes—Merton equation may not be appropriate. To support this idea, Khrennikov builds on a framework of contextual probabilities using agents as a way of overcoming criticism of applying quantum theory to finance.
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.
Chen quantum options and futures exchange a paper in where he presents a quantum binomial options pricing model or simply abbreviated as the quantum binomial model. Metaphorically speaking, Chen's quantum binomial options pricing model referred to hereafter as the quantum binomial model is to existing quantum finance models what the Cox-Ross-Rubinstein classical binomial options pricing model was to the Black—Scholes—Merton model: These simplifications make the respective theories not only easier to analyze but also easier to implement on a computer.
This shows that assuming stocks behave according to Maxwell-Boltzmann classical statistics, the quantum binomial model does indeed collapse to the classical binomial model. Quantum volatility is as follows as per Meyer: Maxwell—Boltzmann statistics can be replaced by the quantum Bose—Einstein statistics resulting in the following option price formula:. The Bose-Einstein equation will produce option prices that will differ from those produced by the Cox-Ross-Rubinstein option pricing formula in certain circumstances.
This is because the stock quantum options and futures exchange being treated like a quantum boson particle instead of a classical particle. From Wikipedia, the free encyclopedia. Statistical Mechanics and its Applications. Journal of Systems Science and Complexity. Reducing the Complexity of Finance". ArXiv Condensed Matter e-prints: Journal of Computational Finance. Physica A Statistical Mechanics and its Applications.
Options, futures, and other derivatives. Upper Saddle River, N. The Journal of Political Economy. Advanced Strategies in Financial Risk Management. Extending and simulating the quantum binomial options pricing model. The University of Manitoba. General areas of finance. Computational finance Experimental finance Financial economics Financial institutions Financial markets Investment management Mathematical finance Personal finance Public finance Quantitative behavioral finance Quantum finance Statistical finance.
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