Does security transaction volume–price behavior resemble a probability wave?

Shi, Leilei

doi:10.1016/j.physa.2005.10.016

Cited by 23 publications

(45 citation statements)

References 30 publications

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“…This was because of that the residential property values collected along the route given mainly depended on the effects of transportation systems and public parks in this work. Not surprisingly, the profile of the property price volatility along the routes of interest can be understood as a wave-like function of urban housing market system, similar to propagation of the transaction volume-price probability wave or the financial pilot wave [ 34 – 36 ]. Observed data on housing prices from government statistics datasets to depict the variance of the housing prices along designated routes taken from USGS National Map Viewer, as described in Fig 1 , for Boston, Milwaukee, Taipei and Tokyo were illustrated in Fig 5 , respectively.…”

Section: Resultsmentioning

confidence: 99%

Lie symmetry analysis of the effects of urban infrastructures on residential property values

et al. 2021

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Due to the complexity of socio-economic-related issues, people thought of housing market as a chaotic nucleus situated at the intersection of neighboring sciences. It has been known that the dependence of house features on the residential property value can be estimated employing the well-established hedonic regression analysis method in teams of location characteristic, neighborhood characteristic and structure characteristic. However, to further assess the roles of urban infrastructures in housing markets, we proposed a new kind of volatility measure for house prices utilizing the Lie symmetry analysis of quantum theory based on Schrödinger equation, mainly focusing on the effects of transportation systems and public parks on residential property values. Based on the municipal open government data regularly collected for four cities, including Boston, Milwaukee, Taipei and Tokyo, and all spatial sampling sites were featured by United States Geological Survey (USGS) National Map, transportation and park were modelled as perturbations to the quantum states generated by the feature space in response to the environmental amenities with different spatial extents. In an attempt to ascertain the intrinsic impact of the location-dependent price information obtained, the similarity functions associated with the Schrödinger equation were considered to facilitate revealing the city amenities capitalizing into house prices. By examining the spatial spillover phenomena of house prices in the four cities investigated, it was found that the mass transit systems and the public green lands possessed the infinitesimal generators of Lie point symmetries Y2 and Y5, respectively. Compared statistically with the common performance criteria, including mean absolute error (MAE), mean squared error (MSE) and, root mean squared error (RMSE) obtained by hedonic pricing model, the Lie symmetry analysis of the Schrödinger equation approach developed herein was successfully carried out. The invariant-theoretical characterizations of economics-related phenomena are consonant with the observed residential property values of the cities internationally, ultimately leading to develop a new perspective in the global financial architecture.

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Section: Resultsmentioning

confidence: 99%

Lie symmetry analysis of the effects of urban infrastructures on residential property values

et al. 2021

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“…. It is exactly the superposition principle of quantum mechanics, which has been studied by Shi [16] and Piotrowski [17] in the stock market.…”

Section: State Vector In the Hilbert Spacementioning

confidence: 98%

A quantum model for the stock market

Zhang

Huang

2010

Physica A: Statistical Mechanics and its Applications

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Beginning with several basic hypotheses of quantum mechanics, we give a new quantum model in econophysics. In this model, we define wave functions and operators of the stock market to establish the Schr\"odinger equation for the stock price. Based on this theoretical framework, an example of a driven infinite quantum well is considered, in which we use a cosine distribution to simulate the state of stock price in equilibrium. After adding an external field into the Hamiltonian to analytically calculate the wave function, the distribution and the average value of the rate of return are shown.Comment: Final accepted version by Physica A. 13 pages and 3 figure

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“…What is surprising is how little we really know about trading volume (Lee and Swaminathan, 2000). Trading volume distributes over a price range in a limited number of patterns on a trading day in stock market (Shi, 2006). So, it is reasonable that the market behaviors could be described in price and volume coordinates (For an illustration of this, see Figure 1).…”

Section: Introductionmentioning

confidence: 99%

“…So, it is reasonable that the market behaviors could be described in price and volume coordinates (For an illustration of this, see Figure 1). It might be governed by the price-volume probability differential equation that is derived from a liquidity utility hypothesis 1 in an economy where traders abide by a trading rule-"price first and time first", i.e., an actual trading price path in a variety of options is selected by the least trading price or cost variation (Shi, 2006). Shi (2006) empirically tests trading volume distribution over a price range on a trading day by two sets of explicit eigenfunctions-analytical and closed form solutions from the price-volume probability wave equation (see a test example in Figure 1).…”

Section: Introductionmentioning

confidence: 99%

“…We extend Shi's price-volume differential equation (Shi, 2006), study the volume uncertainty associated with price, and attempt to solve these questions. We incorporate subjective thinking into the equation, measure the frequency of market crowd's trading action by trading volume probability in terms of principles in behavior analysis (Shi et al, 2010), and test two kinds of adaptive trading hypotheses relevant to the volume uncertainty associated with price.…”

Section: Introductionmentioning

confidence: 99%

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