| Accompanied with the development of contemporary financial theories, classical ones, represented by Efficient Market Hypothesis and Capital Asset Pricing Model, are becoming more and more difficult to make convincing explanations to financial anomalies. Meanwhile, traditional econometric models based on the linear thinking mode are no longer applicable to chaotic economic phenomenon. Considering the volatility of stock market obeys a partial random walk process, scholars proposed a series of methods to analyze it, such as Chaotic Attractive Factor and Hurst index. As far as we known that the chaos theory and the fractal geometry theory are rarely introduced into the researches of finical market. Though they successfully reveal some deficiencies of traditional theories in a certain extent, still, it remains some problems to solve.In this paper, from the perspective of fractal theories, we systematically investigate the internal driving mechanisms of how stock prices fluctuate by analyzing the trend of stock movements in different time scales. Specifically, scaled with one minute, five minutes, thirty minutes, day, week and month, based on the principle of inclusion and coordination rules, we filter out the noises and summed up some significant characteristics of stock prices changes.Some characteristics are defined as follow:1.Top turning point:the highest point in a three low-order K line, the contrary is the bottom turning point.2.Effective connection:there is no K line included between two adjacent turning points.3.Top inflection point (abbreviated as the top):with valid connections, the highest point of a series of adjacent top turning points, the contrary is the bottom inflection point (abbreviated as the bottom).4.Line segment:the effective connection between the adjacent top and bottom. Thus, a segment ling that connects from the bottom to top is called the rising segment, to the opposite, the falling segment5.N-shape:In the same time scale, three adjacent and intersecting line segments construct an N-shape.6.Types of N-shape:In general, the shape of a stock price trend has three shapes. Particularly, when the ending top is higher than all the other points and the rest of the prices are higher than the starting point, which we call as a rising N. Meanwhile, when the ending bottom is lower than all other points and the rest of the prices are lower than the starting point, we take it as a falling N. Then all other N-shapes are named as a consolidation N-shape.An invalid N-connection:when the top of a segment ling which follows a falling N is higher than the bottom of a falling segment, it is called an invalid falling N-connection. On the contrary, it is an invalid rising N-connection. In addition, there is an inverse relationship between the connection segment and the first segment after an N-shape.An extended N-shape:if a segment, following an N-shape, does not meet the conditions of an invalid connecting segment, this segment itself and the adjacent segments are collectively called an extended N-shape segment, which can be continuous extended until it is broken. Thus, all these extended N-shape segments, merged into the third segment of an N-shape, as well as the N-shape itself are called an extended N-shape which is named as a standard N extension. That is to say, an N-shape is shaped when it has been broken. Simultaneously, when the last segment of a standard N-shape, rising or falling, is intersected with at least another two moving averages which are in the same time scale, the price trend has been established. Otherwise, the negative, it is still a consolidation N from.Connection principle:a segment line is either a destructive segment of a standard N-shape, which is deem to lead a new N-shape, or it is included in the previous N-shape.An ally-core:In an N-shape, the region formed by the price that three segment lines intersect together is called as an allied-core which is expressed as:LH (t, n). Where, t is the time scale and n represents the sequence of the two adjacent allied-cores. A consolidation core:if at least9adjacent segment lines have a same price region, a consolidation core has been formed which is represented as PH (t, n). Where, t is the time scale and n represents the sequence of the two adjacent allied-cores. These two cores can be expressed as H (t, n) and a series of consolidation cores are called the consolidation band, which indicates that the price region formed by three ally-cores is a consolidation band. Obviously, the core leaded by an upward segment line is a rising core, otherwise, a falling core.New energy concept:Modern physics believes that everything in the universe is composed by time and energy.The energy of the money is assuming that there are two systems, A and B. A has assets while B has money. When B pays some money to A, assets are transformed from A to B. In this process, the transformation of assets ownership is essentially driven by the energy that occurs in this payment, which is composed by a series of negative price oscillator, representing an unrestrained feature.The intensity of the sentiment force field:a description of the sentiment intensity to the stock price movements, represented as B=B=O/L. Where, q is the number of liquidity price oscillator, v is its speed,0is the flux of the sentiment force line, L is the width of the sentiment force line.We believe that, there are three main N-shapes in stock price movements and each one can be divided into another three subordinate shapes. Just as mentioned above, the results of N-shape movements, including cores, tandem cores and reverse cores, can lead another N-shape in a higher level. Meanwhile, the distribution of cores in the same level obeys the chaos dissipation theory, which means that we can primly predict the stock price movements by vertically analyzing the autocorrelation of different cores.Considering the fact that, in an enterprise, the transformation that assets and money moves is oriented from energy circulations under a certain framework or mechanism. A well-constructed structure can produce more values due to the positive energy coming from equities. Therefore, the so-called value investment is the expectation of positive price oscillators. Based on this theory, PE is the value that the number of negative price oscillators is divided by the annual incremental positive price oscillators. So, through the construction of a stock-trading based energy transformation mechanism, we can conclude that stock prices are determined by the number of price oscillators which representing the maximum quantities of negative price oscillators in each unit of stocks. In other words, stock prices are affected by the scale of net inflow of funds and its distribution.In this paper, principle of dynamics is also introduced into the research to the intrinsic mechanism of stock price movements. We not only investigate the relationship between moving average system and investor sentiment, but also build a "price field theory" and a "sentiment force theory", through which, we establish a model of sentiment and expectations, coming to a price moving equation and new option pricing model. In addition, we make empirical research to all of models listed above.Hereby, we list our main principle as follow:1. Segment length principle:The top and bottom is the point that the stock ion intersects with the price plane when it moves in a3D space constructed by the price&sentiment force field. The connection line from bottom to top is the diameter of the helix circumference. Thus, R=D(v/B).Where, D is the elasticity or duration of the price to capital.v is the speed of price changing while B is the strength of sentiment. Then T=T=2?D/B2. The medium line in an N-shape:An N-shape is a projection of a helical loop in three-dimensional space and its diameter is the second segment in the N-shape. Thus, its equation can follow the principle1.3. The energy of the consolidation core:A consolidation core is a projection when a Three-ring face intersects with the price and the time plane. Thus, the height of the core is the diameter of the face and its length is the same as the consolidation core. Then, the energy can be defined as E=l/h.4. The price of the top:P=[(2R^2-t^2]. Where, R is its radius,Trepresent how long it moves around a circle, P1is its bottom price. Using principle1, we have:P=[(2R2-t2]1/2-P1.5. The price of a call option:assuming that the beginning time of a call option start from the bottom, the cycle of the option is1and the time it moves around a circle is T. Based on principle4, we have:The price of a call option=P (T1/T)-Q. where Q is the financing cost in period T1.In addition, we separate stock price trends into9standard states to describe the physical characteristics of the stock price movements, including the bottom consolidation, escaping from bottom, consolidation rising, accelerate rising, the construction of the top, the construction of the bottom, consolidation falling, accelerate falling and Powei down. Last but not the least; we analyze a series of wildly adopted traditional stock analysis theories by using our N-shape theories in order to demonstrate the progressiveness of our theories. |
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