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# Price Cyclicality Model for Financial Markets. Reliable Limit Conditions for Algorithmic Trading

Authors:
• Algorithm Invest

## Abstract and Figures

Trading the financial markets is a common idea nowadays. Millions of market participants, individuals, companies or public funds are buying and selling different equities in order to obtain profit from the buy and sell price difference. Once the equity was established, the main question marks are when to buy, when to sell and how long to keep the opened positions. This paper will present a mathematical model for the cyclicality of the price evolution. The model can be applied for any equity in any financial market, using any timeframe. The method will gives us information about when is good to buy and when is better to sell. The price cyclicality model is also a method to establish when the price is approaching to change its behavior in order to build limit conditions to stay away the market and to minimize the risk. The fundamental news is already included in the price behavior. Being exclusively a mathematical model based on the price evolution, this method can be easily implemented in algorithmic trading. The paper will also reveal how the cyclicality model can be applied in automated trading systems and will present comparative results obtained in real-time trading environment.
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... The model presented in this paper will use the "Price Cyclicality function" noted as PCY [17]. Starting with the assumption that the price has a wave behavior with variable wavelengths, the model can be successfully applied for any volatile market. ...
... The Price Cyclicality Function (PCY i ) is mathematically defined for each time price series interval (i) by the next recurrent formula, starting from [17]: (4) i Ma and i ma are two moving averages [18] with different periods (Pma and Pma, where PMa < Pma), and (n) is the number of the time intervals considered in the time price series, associated with the period of the presented model. These three parameters (PMa, Pma, and n) are functional parameters that will be optimized for each capital market and for each timeframe used in order to obtain the maximal capital efficiency for a minimal capital exposure, as we will see in a further chapter. ...
... Also, for simplicity, the Signal vector takes 0 and 1 values depending on if the price behavior is up or down. Sample code for the PCY can be found in [17]. ...
Conference Paper
Full-text available
In the first decades of the 21st century, in the electronic trading environment, algorithmic capital investments became the primary tool to make a profit by speculations in financial markets. A significant number of traders, private or institutional investors are participating in the capital markets every day using automated algorithms. The autonomous trading software is today a considerable part in the business intelligence system of any modern financial activity. The trading decisions and orders are made automatically by computers using different mathematical models. This paper will present one of these models called Price Prediction Line. A mathematical algorithm will be revealed to build a reliable trend line, which is the base for limit conditions and automated investment signals, the core for a computerized investment system. The paper will guide how to apply these tools to generate entry and exit investment signals, limit conditions to build a mathematical filter for the investment opportunities, and the methodology to integrate all of these in automated investment software. The paper will also present trading results obtained for the leading German financial market index with the presented methods to analyze and to compare different automated investment algorithms. It was found that a specific mathematical algorithm can be optimized and integrated into an automated trading system with good and sustained results for the leading German Market. Investment results will be compared in order to qualify the presented model. In conclusion, a 1:6.12 risk was obtained to reward ratio applying the trigonometric method to the DAX Deutscher Aktienindex on 24 months investment. These results are superior to those obtained with other similar models as this paper reveal. The general idea sustained by this paper is that the Price Prediction Line model presented is a reliable capital investment methodology that can be successfully applied to build an automated investment system with excellent results.
... A particular approach for risk management techniques that can be used in automated decision-making systems for capital investments can be found in (Vince, 1992). Mathematical models especially designed and optimized for algorithmic trading with proved and sustained results in real capital investments can be found in (Păuna & Lungu, 2018), (Păuna, 2018a), (Păuna, 2018b), (Păuna, 2018c), (Păuna, 2019a), (Păuna, 2019b), (Păuna, 2019c), (Păuna, 2019d), (Păuna, 2019e), (Păuna, 2019f), and (Păuna, 2020). ...
... The Price Probability function was introduced in (Păuna & Lungu, 2018). It was proved that a very strong and direct correlation exists between this function and the price movement. ...
... During this research, the model was tested with excellent results for a considerable number of financial markets: Frankfurt Stock Exchange Deutscher Aktienindex DAX30, New York Stock Exchange Dow Jones Industrial Average Index DJIA30, Financial Times London Stock Exchange Index FTSE100, Cotation Assistée en Continu Paris Stock Exchange Index CAC40, Swiss Market Index SMI20, Standard & Poor's Index S&P500, National Association of Securities Dealers Automated Quotations NASDAQ100, Tokyo Stock Exchange index NIKKEI225, and Australian Security Exchange Index ASX200. For more volatile markets as spot gold (XAUUSD) and currency markets, the signals built with the PPP function must be filtered by additional limit conditions imposed with the Price Cyclicality Function (Păuna & Lungu, 2018). ...
Conference Paper
Full-text available
Capital investment is a sustained activity nowadays. After the worldwide release of the electronic trading systems, automated decision-making investment software is the new trend in financial speculation. A significant part of capital trading is fully computerized today. The buying and selling orders are made and sent automatically, almost in real-time. The price evolution is analyzed by servers using advanced mathematical algorithms. This paper will present one of these models named Price Probability Predictor. It is a method to build a probability field based on the price history and the real-time price action. The revealed function will generate the current probability of a price growth in the next time intervals. Automated entry and exit signals and market limit conditions will be built using the new indicator, in order to automate the whole investment process. Capital investment results will also be included in the current paper to qualify the presented trading methodology and to compare it with other similar models. In conclusion, it was found that the Price Probability Predictor is a reliable mathematical algorithm that can assist any trading decisions, in both ways, manual or automatic capital investments.
... The model presented in this paper will use the "Price Cyclicality function" noted as PCY [17]. Starting with the assumption that the price has a wave behavior with variable wavelengths, the model can be successfully applied for any volatile market. ...
... The Price Cyclicality Function (PCY i ) is mathematically defined for each time price series interval (i) by the next recurrent formula, starting from [17]: (4) i Ma and i ma are two moving averages [18] with different periods (Pma and Pma, where PMa < Pma), and (n) is the number of the time intervals considered in the time price series, associated with the period of the presented model. These three parameters (PMa, Pma, and n) are functional parameters that will be optimized for each capital market and for each timeframe used in order to obtain the maximal capital efficiency for a minimal capital exposure, as we will see in a further chapter. ...
... Also, for simplicity, the Signal vector takes 0 and 1 values depending on if the price behavior is up or down. Sample code for the PCY can be found in [17]. ...
Article
Full-text available
In the first decades of the 21st century, in the electronic trading environment, algorithmic capital investments became the primary tool to make a profit by speculations in financial markets. A significant number of traders, private or institutional investors are participating in the capital markets every day using automated algorithms. The autonomous trading software is today a considerable part in the business intelligence system of any modern financial activity. The trading decisions and orders are made automatically by computers using different mathematical models. This paper will present one of these models called Price Prediction Line. A mathematical algorithm will be revealed to build a reliable trend line, which is the base for limit conditions and automated investment signals, the core for a computerized investment system. The paper will guide how to apply these tools to generate entry and exit investment signals, limit conditions to build a mathematical filter for the investment opportunities, and the methodology to integrate all of these in automated investment software. The paper will also present trading results obtained for the leading German financial market index with the presented methods to analyze and to compare different automated investment algorithms. It was found that a specific mathematical algorithm can be optimized and integrated into an automated trading system with good and sustained results for the leading German Market. Investment results will be compared in order to qualify the presented model. In conclusion, a 1:6.12 risk was obtained to reward ratio applying the trigonometric method to the DAX Deutscher Aktienindex on 24 months investment. These results are superior to those obtained with other similar models as this paper reveal. The general idea sustained by this paper is that the Price Prediction Line model presented is a reliable capital investment methodology that can be successfully applied to build an automated investment system with excellent results.
... In the first part of the paper, the prediction model will be described and explained. Computing a price prediction line is the core of the model based on the price cyclicality function [4]. The prediction model is presented in the form of two bands, one for the stop loss and one for the take profit price levels. ...
... The concepts used in this chapter are not new. The Price Cyclicality (PCY) function was presented for the first time in [4] and represents a function describing the cyclical behavior of the price movement and the intervals when the price is approaching to change its direction. The PCY function can be used in order to set limit conditions to entry and to exit the markets. ...
... min min (4) in which MA and ma represent the moving averages [6] with two different periods. In (3) and (4), the term N is the period of the cyclicality function and represents the number of the time intervals taken into account to build the PCY function; α is a functional parameter that can be optimized for each financial market in order to obtain the best results. ...
Article
Full-text available
After the widespread release of electronic trading, automated trading systems have become a significant part of the business intelligence system of any modern financial investment company. An important part of the trades is made completely automatically today by computers using mathematical algorithms. The trading decisions are taken almost instantly by logical models and the orders are sent by low-latency automatic systems. This paper will present a real-time price prediction methodology designed especially for algorithmic trading. Based on the price cyclicality function, the methodology revealed will generate price cyclicality bands to predict the optimal levels for the entries and exits. In order to automate the trading decisions, the cyclicality bands will generate automated trading signals. We have found that the model can be used with good results to predict the changes in market behavior. Using these predictions, the model can automatically adapt the trading signals in real-time to maximize the trading results. The paper will reveal the methodology to optimize and implement this model in automated trading systems. After tests, it is proved that this methodology can be applied with good efficiency in different timeframes. Real trading results will be also displayed and analyzed in order to qualify the methodology and to compare it with other models. As a conclusion, it was found that the price prediction model using the price cyclicality function is a reliable trading methodology for algorithmic trading in the financial market.
... It was found that additional condition to avoid the extreme price will significantly improve the trading results and will increase the efficiency of the trading system. A proper mode to avoid these intervals is to use the "Price Cyclicality" function presented in [6]. Noting with where ξ and φ are two functional parameters that can be optimized for each market in order to avoid opening orders into overbought and oversold intervals. ...
... This parameter is the period considered to build the cyclicality function. More considerations about it can be found in the author source [6]. The signals (3.2) can be used for both AT and HFT. ...
... The first improvement must be made in order to avoid the overbought and oversold price intervals. For this purpose, we used the price cyclicality function [6]. The second improvement must be made in order to avoid opening trade in weak price trends. ...
Article
Full-text available
... Average (Cox, 1961), BB -Bollinger Bands (Bollinger, 2002), or PCY -Price Cyclicality Lungu, 2018). For each time interval in the time price series, these functions will take a value. ...
... More considerations to include limit conditions in automated capital investment s stems are presented in (P una & Lungu, 2020). In (P una & Lungu, 2018), are presented trading results obtained with and without the limit conditions built with the (PCY) function. We can conclude that the advantages of using limit conditions with Price Cyclicality Function are evident if we analyze those results. ...
Thesis
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After several attempts to publish my Ph.D. thesis with different prestigious publishers, I have decided to make this work public and free of charge for anyone. Enjoy! Cristian Păuna
... For the currency and commodity markets, reliable trading models that can be automated and included in investment software can be found in [7], [8], and [9]. Original data-mining methods, especially designed and optimized for automated capital investment software, can be found in [10]- [19]. Investment signals are built using all of these models by analyzing the realtime price series. ...
... This research has identified more limit conditions methods to filter these cases. To exemplify, in figure 3 was drawn the method to build limit conditions using the Price Cyclicality Function (PCY) introduced in [19]. No new investments trades will be opened if the PCY function overtakes a specified limit value: ...
... Moreover, the introduced function can be computed in real-time and can be implemented in any automatic capital investment software system. A reliable mathematical model to study the cyclical behavior of the price market was introduced in (Păuna & Lungu, 2018). This paper will apply the same model for trading volume information. ...
... The best solution was found by using the Price Cyclicality function (Păuna & Lungu, 2018). The ascending periods of the PCY function are in a strong and direct correlation with the price evolution, as the authors proved in the introduction paper of the Price Cyclicality model. ...
Article
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Capital investment is a sustained activity nowadays. The buy and sell decisions are usually made in technical analysis using the price quote evolution in time. Another useful information provided by any stock exchange is the trading volume for each time interval. The volume information is usually hard to be included in a trading or investment strategy, having an unstable and discontinued evolution in time. Some obsolete ideas indicate a favorable entry period after a maximal traded volume value interval, but today, on the high price volatility markets, when a maximal value is detected, usually is too late for a convenient price entry on that market. This paper presents a mathematical model specially designed for fast and instant market entry decisions based only on the traded volume information. It was found that even the traded volume variation in time is discontinued, a cyclical phenomenon is present in all markets. With the proper mathematical method, the Volume Cyclicality function can be computed in real-time in order to build reliable capital investment signals. The model presented in this paper fills an essential gap in the literature, and it was tested for more than ten years on the most important stock exchanges in the world. Investment results are also included in this paper to prove the efficiency and utility of the presented method. The Volume Cyclicality function is an exclusively mathematical model, and it can be applied in any automated investment software system to improve capital efficiency.
... For the currency and commodity markets, reliable trading models that can be automated and included in investment software can be found in [7], [8], and [9]. Original data-mining methods, especially designed and optimized for automated capital investment software, can be found in [10]- [19]. Investment signals are built using all of these models by analyzing the realtime price series. ...
... This research has identified more limit conditions methods to filter these cases. To exemplify, in figure 3 was drawn the method to build limit conditions using the Price Cyclicality Function (PCY) introduced in [19]. No new investments trades will be opened if the PCY function overtakes a specified limit value: (4) A particular type of limit conditions to avoid trading near-maximal price levels can be made limiting the distance between the current price level and an adequate price trend line. ...
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Using automated capital investment software systems is a common task today. At the beginning of the third millennium, modern investors are using artificial intelligence resources and methods to find the best investment opportunities on capital markets and to process the trading orders. One of the most important aspects of this activity, besides the buying and selling decisions, is to stay away from the market risk in specific conditions. For this purpose, in the current doctoral research, the notion of limit conditions in capital markets was introduced by the authors. On the high price volatility markets, when the economic or geopolitical background is changing fast, real-time decisions for earlier investment closing, or filtering decision not to open new positions in specific market states, will contribute together to the risk reduction and will provide a higher capital efficiency a the long time run. In the real-time investment software systems, the limit conditions method's implementation presumes particular aspects in order not to introduce additional time delays for the trading orders. This paper will present the way how to include additional limit conditions procedures into automated algorithmic trading software systems. It was found that any investment strategy can be improved by using the limit conditions methods presented in this paper. Based on particular data-mining methods applied to real-time price series of any market, these methods can be automated and included in any capital investment informatics systems in order to improve the results and to reduce the allocated capital risk.
Chapter
Capital investment is a sustained activity nowadays. After the worldwide release of the electronic trading systems, automated decision-making investment software is the new trend in financial speculation. A significant part of capital trading is fully computerized today. The buying and selling orders are made and sent automatically, almost in real-time. The price evolution is analyzed by servers using advanced mathematical algorithms. This chapter will present one of these models named Price Probability Predictor. It is a method to build a probability field based on the price history and the real-time price action. The revealed function will generate the current probability of a price growth in the next time intervals. Automated entry and exit signals and market limit conditions will be built using the new indicator, in order to automate the whole investment process. Capital investment results will also be included in the current paper to qualify the presented trading methodology and to compare it with other similar models. In conclusion, it was found that the Price Probability Predictor is a reliable mathematical algorithm that can assist any trading decisions, in both ways, manual or automatic capital investments.
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The most important part in the design and implementation process of automated trading systems in any financial investment company is the capital and risk management solution. Starting from the principle that the trading system must run fully automated, the design process gets several particular aspects. The global stop loss is a special approach for the risk management strategy that will ensures a positive expectancy in algorithmic trading. A case study based on an already optimized trading algorithm will be used to reveal how important the risk level optimization is, in order to improve the efficiency of the trading software. The main optimal criteria are as usual the profit maximization together with the minimization of the allocated risk, but these two requirements are not enough in this case. This paper will reveal an additional optimization criterion and the main directions to build a reliable solution for an automated capital and risk management procedure. Keywords: automated trading software (ATS), business intelligence systems (BIS), capital and risk management (CRM), algorithmic trading (AT), high frequency trading (HFT). (Available at: https://pauna.biz/Capital_and_Risk_Management)
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The mean square error of prediction is calculated for an exponentially weighted moving average (e.w.m.a.), when the series predicted is a Markov series, or a Markov series with superimposed error. The best choice of damping constant is given; the choice is not critical. There is a value of the Markov correlation ρ0 below which it is impossible to predict, with an e.w.m.a., the local variations of the series. The mean square error of an e.w.m.a. is compared with the minimum possible value, namely that for the best linear predictor (Wiener). A modified e.w.m.a. is constructed having a mean square error approaching that of the Wiener predictor. This modification will be of value if the Markov correlation parameter is negative, and possibly also when the Markov parameter is near ρ0.