News and Behavioral Impact on Commodity Markets through Multi-Agent Modeling

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News and Behavioral Impact

on Commodity Markets

through Multi-Agent

Modeling

MSc Thesis

Submitted to obtain the MSc degree in Computational Science

Author: Semen Semenov

Student nr: 10874739

E-mail: semyonov@post.su

Date of defense: 28th of August, 2015 Supervisors:

Dr. Drona Kandhai (UvA) Dr. Svetlana Borovkova (VU)

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Chapter 1. Introduction

Modern financial theories are based on propositions about both the macroscopic and microscopic financial market structure. On the macroscopic level, numerous researches assume efficient market hypothesis, which is also known as the random walk hypothesis. The random walk hypothesis implies that stock prices follow a random and unpredictable path, with equal probability of up and down movements, normal distributions of price changes and without the impacts of previous market data (Kendall, 1953). The validity of the hypothesis has huge effects on trading strategies, because the hypothesis reveals the impossibility of a prediction of future prices. The idea that new information almost instantaneously aggregates into the price lies in the basis of the efficient market hypothesis. In other words, it is impossible to develop a trading strategy that can make more profits than average without taking an additional risk.

Fama’s works on different markets (1970) show that the returns of stock often do not follow a random walk. For example, Smith and Ryoo (2003) tested the weekly data for several European countries which covers the period from April 1991 to August 1998, and they found that four out of five countries, viz., Greece, Portugal, Poland and Hungary, rejected the random walk hypothesis, although the market of Turkey followed a random walk. Thus, it is sufficient to assume that the random walk hypothesis is not the best assumption for modeling the price dynamics.

Following the intuitional and empirical evidences, behavioral counter arguments of the theory were elaborated. The behavioral modifications relate to the micro (participant) level of market. In rational theories, the agents either behave fully rationally or an aggregation of behavior of irrational agents gives the rational results in the long-term. In contrast, behavioral theories imply irrational or bounded rational behaviors of participants. In this study, prospect theory is used as a basis of the decision making process of the agents.

The next component that we will investigate is participants’ perceptions of news. The implementation of this component will significantly increase the prediction accuracy of models of irrational agents. So far, it is not systematically developed in multi-agents models. For the purpose of the investigation of its impact, news of commodity data from Thomas Reuter Analytics is used. The data contains information of specific commodities for a specific period of time. Each news element represents a single news item from the newspaper or another electronic news source where an element includes a list of specific attributes. The most important things for the research are the relevance and the sentiment of news. The parameters are used to measure the impacts of news on agents in the model. The relevance refers to the degree of the relationship

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between news and stock, while the sentiment represents that the news has some elements affecting the participants to hold a negative or a positive mood. The findings show how these two parameters influence the agents in the model and change their behaviors.

Overall, the objective of the research focuses on the creation and the testing of a multi-agent model which would allow a prediction of market dynamics of the specific commodity. The model includes tools for the elaboration of the news and the behavioral components for the agents.

1.1. Research aims and questions

The main aim of this research is to investigate the impacts of the news on the commodity market using multi-agent modeling. The method allows to study the impacts of the news as a factor of price dynamics, and allows predicting future dynamics using agents with calibrated parameters. The secondary goal is the demonstration that prospect theory can be used as an adequate mechanism for the introduction of personal characteristics for participants in a market. The result of this research is a framework for price modeling using news data.

We aim to answer several research questions ranging from details about the parameters of the agents to the structure of the market as a whole and the impacts of news on the market.

The research studies different commodity markets for which data is available through the following questions:

1. With what accuracy the multi-agent model with parameters for agents, news and market estimated from real data can predict the commodity price dynamics? (Main question).

2. What prospect theory utility function has the best predictability properties? 3. How do the relevance and the sentiment of news affect the price?

4. What initial proportion between fundamentalists and chartists is the most suitable for the market?

5. What speed of the price dynamic process is the most suitable for the market? The speed of the process is a ratio of excess demand at the particular time step to changes in prices between the time step and the previous.

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This thesis focuses on the investigation of the questions by creating a framework for the news analyses. First, the literature review argumentations and critics about all covered components of the framework which have been given. The rest of this thesis describes the creation, the implementation and the robustness of the model.

The thesis is structured as follows; the next chapter gives a detailed description of the three parts of the model, viz., news impact analysis, multi-agent models and personal features of the agents, namely prospect theory utility functions. Then, chapter 3 provides the model developed in this research, which is based on the findings from the second chapter. In addition, this chapter also shows the calibration of the model. The fourth chapter is the practical applications of the model, including the discussions of the limitations and the robustness of the model. The conclusions and the recommendations are presented in the last chapter.

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Chapter 2. Overview of related studies

2.1. News and market

The classical market theory assumes that a market is effective and the impact of news in the market is accumulated in the price almost immediately. More modern theories assume that because of the bounded rationality of human beings, the markets are not rational and the news does not have an immediate and a linear impact on the price. Thus, the impact has to be studied in a non-linear, behavioral perspective.

The structures of the news can be divided into two parts: the news itself and events behind the news. According to the oxford dictionary, an event is defined as “a thing that happens or takes place, especially one of importance”. Events are important objects for researchers. For example, Radinsky et al. (2012) study the relationships between events. They create a system for predictions of dependent events based on natural language processing and data analysis. The events often do not have a significant impact on the behavior of people, because people do not receive full information about events directly. However, for the news, things are different, since people can receive news information through proxies such as newspapers, video and photo sources and news agencies easily.

For all news sources, the newspapers and the other text sources are the most suitable for analysis and therefore the most attractive for researchers. Because of this reason most of the studies as well as this research use data from this type of news. Actually, the news and the relationship between the news and a market dynamic are popular topics in the science community. Those studies reveal dependencies between news of different type and the dynamics of prices.

2.2.

Structure of the news

One of the ways of investigating the impacts of news is dividing the news into categories and analyzing the impacts of each category. For example, Bollen et al. (2010) demonstrate the impacts of the moods of twitter messages on the stock market. They show the correlation between Dow Jones Industrial Average (DJIA) and sentiments of the messages. Two tools are used in their research, the first one divides messages into positive and negative sentiments and the other uses six types of moods, from calm to happy. They find that the correlation between DJIA and categories of the second type is much stronger than that between DJIA and the first category. In addition, the research shows some special cases where a mood predicts changes in stock dynamics with accuracy of 87.6%. The analysis of sentiments in natural gas futures is

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developed by Borovkova and Mahakena (2015). They investigate the impacts of the sentiments of the news, following a translation of a sentiment of news represented as a positive, negative or neutral signal. They show that the sentiments have strong impacts on both stock price and volatility. The division of the news to categories relating to sentiments is highly developed in literature, see also Veronesi (1999), Birz and Lott (2011) and Medovikov (2014).

Other authors show that markets can react differently to similar events in different periods. Veronesi (1999) argues that the market price overreacts to bad news when the price is high and vice versa. Birz and Lott Jr (2011) analyze the reactions on the news about increase of GDP during recession and economic boom. Their study shows that the market dynamics differs greatly in the cases of recession and economic boom, and the positive news has much more impacts in the periods of recession while the negative news has the strongest impacts during the booms.

They explain that the news has impacts on mood, namely positive news increases optimism while negative news increases the overall pessimism, which leads to the observed behavior. From this point of view, the cases seem to be logical. Because in a good situation the overoptimism exists, thus the pessimistic news has greater impacts on market and vice versa.

Beechey and Wright (2009) propose to divide all news into three categories: news about prices, real side of the economy and monetary policy. The authors confirm the expediency of this approach by finding their differences in impacts to the real rates and the rates of inflation compensation. According to the research, the news about price has an effect on inflation compensation, the news about real-side of economy affects the real yields and news about monetary policies has effects on both the rates and the compensation of inflation.

Tetlock (2008) reveals that the news contains not only new information, but also old information. He confirms the hypothesis that the market overreacts to the stale information and underreacts to the new information. The conclusion of the research contradicts the idea that a market should reflect all available information (Fama, 1970). In other words, it can be considered as evidence against the efficient market hypothesis.

Other studies show the differences between the private and the public information, for example Vega (2004) and Daniel et al. (1998). These authors find the evidences that people tend to overreact to private information, because of their strong beliefs in the private sources of information, and underreact to the public information. As a result the informed traders who have access to the private information already changed the price before the day of the public announcement.

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In addition to these categories, many others categories can be considered, for example the classification of the news about earnings and the news about accruals (Hirfshleifer, 2011).

The categorization of news in this research is similar to the approach adopted by Borovkova and Mahakena (2015). That is to say, the news is divided into positive, negative and neutral elements. Each element of news has a value of sentiment ranging from 0 to 1.

Although the news shares the similar structures, the approach to the analysis of the news’ impact differs completely in this research. Briefly, the studies described above focus on the problem of finding the relationships between the news of a specific category and the price dynamic. The statistical approach is used to deal with this problem. Through this approach, they extract useful data about specific categories of news and observe the interconnections between the news and the market. According to these descriptions, it is easy to find that this research shifts its focus to inner reaction of the market to the news. Thus, the problems for this research are what structure of market, how do individual investors react to news and how do the individual agents generate the market dynamics through interactions between each other.

Since the research concerns the inner reaction of the market to the news, our focus moves from the macro level of analysis to the micro level obviously. Because of the specific questions and aims related to the structures of markets and to the predictions of the dynamics of the price, the statistical approach is not suitable. Instead, we adopt the multi-agent simulation. The multi-agent model allows an observation and an analysis of the problems on both the micro and the macro level. Further, the models also provide an opportunity to obtain answers to the questions about market structures and impacts of news. The multi-agent modeling is discussed in the section “Multi-agents models in stock market”.

2.3. Perception of the news

This section describes the participants’ perceptions of news in the market by examining the theories of perception of news in terms of psychology of human beings.

The behavioral property of limited attention is examined in this section. A person who has this property cannot accept all available information because the person has the limits in perception of the information. Thus, a market participant should filter the news about market and focus only on the most important piece. Moreover, many researches show that even professional investors ignore the crucial news. The person who has this property and other behavioral features and thus has bounded rational mind is called a bounded rational agent (Simon, 1955).

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Barber and Odean (2008) show that inattention plays a critical role in buying a stock. They observe the trend that investors buy a stock according to the previous day's traded value. They try to find the tendency of overbuying a stock in the cases when the trading volume of the previous day was low or high. The presence of news does not have a significant effect on this tendency.

Moreover, some scholars find that the investors are even more inattentive to subtle economic links (Cohen and Frazzini, 2008). They argue that the traders miss the important news about the main customer of a company. As a result the time gap between the announcement of the problems of the customer and the drops in price of the stock can reach several months.

Amounts and types of attentions are not constant and they depend on different factors. DellaVigna and Pollet (2009) investigate the effects of Fridays on the attention. They find that there is a big difference between returns and volume of the stock after the news announcements on Friday and non-Friday.

The limited attention is an important feature of the human mind and it is strongly connected with the perceptions of news. Furthermore, the limited attention is a good illustration that people are not fully rational and thus the impacts of news should not be developed in the model under the fully rational perspective. Instead of this, the bounded rational approaches are elaborated in this research through the introduction of prospect theory utility function which represents the characteristics of the agents. The behavioral facts from this chapter is expanded and complemented in the section “Rational market and prospect theory”.

2.4. Multi-agents models in stock market

Compared to the classical macroscopic modeling, the agent-based modeling approach simulates both the dynamics of population and the heterogeneity of individuals. The approach is used in finance for the investigation of the behavior and the survivability of the participants.

A part of the studies focuses on the broad activity of a group of agents for a trading institution. Yuan et al. (2002) create a large system of decision making for stock trading. Their framework contains several types of agents, such as agents of fundamental or technical analysis, agents for monitoring, risk management and coordination. In addition, they add agents for interaction with sources of information such as the Internet. Therefore, the model covers the full chains of the trading process, from information to decision makers. They show that the model can make high quality decisions based on the interaction of agents.

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Garcıa et al. (2000) create a system for implementation of high-level stock trading strategies. In their framework agents interact with the Internet, use the knowledge of finance and try to achieve their desired goals. Their research focuses on the creation of the decision making system for the agents of the same type instead of using a specific logic for different type of agents.

Seo et al. (2004) develop a system for an intellectual portfolio management. The focus in their study shifts to the news analysis for the purpose of monitoring portfolio related events. The aim of their research is detecting changes in the news related to companies in the portfolio. For the purpose, text mining techniques and agents who analyze news are used.

The studies above focus on specific financial institutions. Furthermore the news analysis is developed slightly or it is not developed at all. The following studies focus more on a market overall rather than on internal agents of institutions.

The participants in the market can be divided into different categories. The representation of a market as a set of chartists and fundamentalists is the most popular method (Frankel and Froot, 1990; Brock and Hommes, 1998). In these models a chartist is an agent who considers time series of price and follows trends in the price dynamics and a fundamentalist is assumed to have knowledge of the real price of the stock and make money in terms of the fluctuations of stock prices.

Consider a model with the chartists and the fundamentalists, transitions between the states and the dynamics of the price formed by the agents (Alfi et al., 2009). The authors name the model “Minimal agent based model for financial markets”.

In their model, chartists observe a trend and try to guess a price at the next period. The price at the next period 𝑝_𝑡+1 for chartists:

𝑝𝑡+1 = 𝑝𝑡 + 𝑏 𝑀 − 1(𝑝𝑡− 𝑝𝑀𝑡) + σεt 𝑝𝑀𝑡 = 1 𝑀 𝑝𝑡−i 𝑀−1 𝑖=0

where 𝑝_𝑡 is the price at time t, b denotes the activity of chartists (strength of the force of actions of chartists), 𝑝_𝑀_𝑡 is the moving average performed on the previous M time steps, ε_t is a white noise and σ is the amplitude of this noise.

Fundamentalists calculate the price based on the fundamental value 𝑝_𝑓: 𝑝_𝑡+1 = 𝑝_𝑡 + γ(𝑝_𝑓 − 𝑝_𝑡) + ζε_t

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where 𝑝_𝑡 is the price at time t, γ is the activity of fundamentalists (strength of the force of actions of fundamentalists), εt is a white noise and σ is the amplitude of this noise. The noise and the amplitude are common for both type of agents.

An agent can change its type from chartist to fundamentalist and vice versa. The transitions probabilities for type changing:

𝑃_𝐶𝐹 = β(1 + δ) K + NF

N , 𝑃𝐹𝐶 = β(1 − δ) K + N_c

N , N = NF+ Nc

β − the speed of the switching processes, NF and Nc− numbers of fundamentalists and chartists, δ −an asymmetric parameter for markets, where the fundamentalists have more power than chartists, K is the parameter for prevention of metastable states. In the metastablestates the system converges into two states: full chartists market and full fundamentalist market.

Quart (1993) shows that the transition behavior depends on 𝜀 = 𝐾𝑁. More precisely the system reveals the most suitable behavior when 𝜀 > 1. First group of plots below demonstrates the probability distribution for the ratio of chartists over the whole population. The second group shows ratio of the chartists over time.

The first group confirms that if epsilon is less than 1, the system remains in a metastable state most of the time. If epsilon increases, the distribution of the fraction converges to normal distribution. Second group shows similar results in time.

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Figure 1. Relative frequency of fraction of chartists for increasing epsilons. The epsilons equal

to 0.1, 1 and 10 respectively, the Ks change according to the equation 𝐾 = 𝜀

𝑁, the other

parameters are fixed. The fraction of chartists is a ratio of chartists to the whole population

𝑁𝑐

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Figure 2. Relative frequency of fraction of chartists over time. The epsilons equal to 0.05, 0.5

and 5 respectively, the Ks change according to equation 𝐾 = 𝜀

𝑁 the other parameters are fixed.

The time axis is enumerated in numbers of rounds of the simulation, and the chartists’ fraction is a ratio of chartists to the whole population Nc

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The last element of the model is the formation of the price dynamic through excess demand. In this chartist-fundamentalist model, the excess demand ED is simply proportional to the price signal of chartists 𝐸𝐷_𝑐 and fundamentalists 𝐸𝐷_𝑓. The price signals are the difference between the prices at the next period and at the current period 𝑝_𝑡+1 − 𝑝_𝑡. As a result, the price at the next period depends on the excess demand, the price at the current period and the random terms. Specifically, the price evolves as follows:

𝑝_𝑡+1 = 𝑝_𝑡 + ED + ζε_t ED =NF N γ(𝑝𝑓 − 𝑝𝑡) + N_c N ( b M − 1𝑝𝑡− 1 𝑀 𝑝𝑡−i 𝑀−1 𝑖=0 )

Where N_F,N_c, N represent the quantity of fundamentalists, the chartists and overall population size respectively, the other parameters are similar to the price equations for fundamentalists and chartists.

The chartist-fundamentalist model provides significant basis for the research, but the model does not have two important features: news factor and personal behavior factors.

In this research the news is proposed as the main factor of changes in price. Thus it should take the formation of excess demand into consideration. Because the model assumes that chartists do not observe the news and just follow the trend, the factor of news has to be transferred to the behavior of fundamentalists. In other words, the fundamentalists seek changes in the fundamental value because of new information.

The other factor is the personal behavior factor. Although the chartist-fundamentalist model implies that the model exists on both micro and macro levels, the most of the dynamic exhibits on macro level. The individuals form demand on micro level based on decision making rules, but the main elements of price dynamics, namely the chartists and the fundamentalists activity parameters b and γ, reside on macro level. In addition, in their model agents follow the rational rules, but in this research the opposite is assumed.

The model has to be significantly developed and changed for the purposes of this research.

2.5. Rational market and prospect theory

The rational market theories are the classical theories of the market. According to the classical principle, a participant of economic relationships has pure rational logic and the person is trying to maximize the profits. John Stuart Mill uses the term “economic human” for the type of

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participants (Persky, 1995). In the 20th century the idea of the economic human was elaborated in many financial theories. In the chronological order, the Efficient market hypothesis (EMH) developed in the 1960s says that the price of financial assets reflects all available information and follows Michael Jensen’s remark who considers EMH as a hypothesis with the strongest empirical evidences in economics. Next, the same idea lies in the basis of the Black-Scholes model discovered in 1978. After that, many modern researchers adopt the assumptions about rationality in the market (Yen and Lee, 2008). However, there are also some researchers who propose that a market is not rational or the market is not completely rational, because of the nature of human beings. The field of studies named behavioral economics considers participants of the market as bounded rational creatures.

The behavioral economics and behavioral finance describe cognitive, social and emotional factors in decision making of individuals. Herbert Simon, one of the discoverers of the behavioral economics, maintains that individuals are not looking for maximization of their profit from the actions. Instead, people are satisfied with “good enough” depending on their emotional and cognitive feelings. According to the opinion of the author, the individuals cannot assimilate and analyze all the information needed for the optimal decision making. In addition, he states that it is not only the limit in the information access, but also the “cognitive limits” for the perception of the information. As a result, together with time restrictions for decision making, it leads to non-optimal decisions.

The ideas about features of bounded rationality are developed in studies of Kahneman and Tversky. The researchers conduct series of experiments for verification of Von Neumann-Morgenstern axioms of preference. The experiments show that the empirical data does not agree with the axioms.

The one of the first experiments conducted by Kahneman and Tversky (1979) considers the following situation. A participant must choose between two options in the two gambles:

Gamble 1:

Option A:100% chance of losing $3000. Expected value E[A] = - $3000.

Option B: 80% chance of losing $4000and 20% chance of losing nothing. E[B] = - $3200.

Gamble 2:

Option C:100% chance of receiving $3000. E[C] = $3000.

Option D: 80% chance of receiving $4000, and 20% chance of receiving nothing. E[D] = $3200.

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From the rational perspectives of expected utility theory of Neumann and Morgenstern (1944), most of the people have to prefer Option A in Gamble 1, because E[A] > E[B] and Option D in Gamble 2, because E[D] > E[C]. However, the experiments show that 92% of respondents choose B and 80% choose C. Similar results were obtained from numerous experiments of these authors and others (Barberis, 2012).The results of the experiments lead to a confirmation that people do not always choose the optimal strategy and get such a conclusion that preference of the people over negative prospects is not a mirror image of their preference over positive prospects. Moreover, the participants show risk-averse behavior in gains and the people become risk-seeking during losses.

The next part of the prospect theory can be described through the experiment (Kahneman and Tversky, 1979). The participant faces the following gamble:

50% chance to win $150, 50% chances to lose $100.

Most of the people reject the gamble with equal chances to win and lose. Furthermore, they accept the gamble only in cases when a possible win is at least twice as big as the possible loss (Tversky and Kahneman, 1992). Although the prospect theory includes different behavioral parts, the examples above give sufficient background for this research. As the result, the summary of these findings is given in form of the prospect theory utility function.

Overall, prospect theory utility functions have several specific properties:

1) In the positive domain the function is concave, because of the risk aversion of individuals.

2) In the negative domain the function is convex, because of the risk-seeking behavior. 3) The function is steeper for losses than for gains, because the losses hurt people more than the gains pleases them.

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Figure 3. An example of prospect utility function from Kahneman (2003). The function is

described as a graph in which the concave represents gains, convex for losses and the line is steeper in the domain of losses than that in the domain of gains.

In practice several prospect theory utility functions are used. The functions do not always reveal all the properties of prospect theory functions but often show a good approximation of the theory and of the empirical data. Among them, the most popular functions are the logarithmic function, the power function, the quadratic function and the exponential function (Stott, 2006).

2.6. Utility functions

2.6.1. Logarithmic utility function

The logarithmic utility function was proposed by Bernoulli in the eighteenth century and the function is one of the first utility functions (Bernoulli, 1954). The inventor of the function notes the property of declining of marginal utility. Before the study, the linear utility was broadly accepted. In other words the proposition that the increase in the utility does not depend on the absolute value of the argument was accepted. The basic proposition inside the logarithmic utility is that the increase in inverse ratio related to the absolute value of the argument. In terms of prospect theory, a participant with the utility function has risk aversion behavior. Bernoulli gives an example of a lottery ticket with 50% chance to win money and 50% chance to receive nothing and he gives empirical evidences that decision about purchasing of the lottery ticket does not depend solely on expected value, but on individual utility function based on the wealth of the person. As a result, he says that any increase in goods will always result in increase in utility, but the increase is inversely proportional to the overall utility. In other words, a person who received

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the amount of money has more fun than a richer person and the opposite is true for losses. The function can be written for domains of positive and negative numbers as follows:

𝑈 𝑥 = ln α + 𝑥 ; α + 𝑥 > 0

λ ln(−(𝑎 + 𝑥)); α + 𝑥 < 0

Figure 4. Logarithmic utility function with the parameters shown in the inset.

2.6.2. Power utility function

The power utility function is widely accepted in the fields related to human behavior since Stevens (1957). The author suggests the usage of the power function for the measurement of the magnitude of a physical stimulus for human beings. In his research the power function shows good results in approximations for analysis of human senses and he concludes that the power function interprets psychological magnitudes better than the logarithmic function.

The function is the most popular function in the behavioral finance. It is widely used as an approximation of results for the experiments within the prospect theory (Luce, 1991; Wakker and Tversky, 1993; Tversky and Kahneman, 1992). They claim that the function has all properties of prospect theory functions and show good accuracy in approximation of real data.

Opposite to the logarithmic utility function, the marginal utility for the power utility function is a constant. Thus, in practice the value of the function is unlimited. The piecewise utility function is described by the following equations:

𝑈 𝑥 = x α_{; 𝑥 > 0} – λ(−x)α; 𝑥 < 0 -6 -5 -4 -3 -2 -1 0 1 2 3 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

alpha = 1, lambda = 2.25

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Figure 5. Power utility function or the parameters shown in the inset.

2.6.3. Quadratic utility function

The quadratic utility function can bind the parameters of the function with statistical data: expected value of wealth and standard deviation of the value (Bell, 1995 and Zakamouline, 2008).

𝑈 𝑥 = x − a𝑥

2_{; 𝑥 > 0}

λ(x + a𝑥2_{); 𝑥 < 0}

Although the function is highly useful in finance, this form has several major drawbacks. The most obvious disadvantage is that 𝑈 𝑥 is not always positive when parameter x is positive and vice versa. Thus the parameter for the function has to be chosen in this interval, because the function is bounded for usage in prospect theory. This specific property of the function is shown in figure 3. Rieger and Bui (2011) argue that the function can be cut and replaced by another function in these areas. The trick solves the problem, but makes the function even more difficult.

-25 -20 -15 -10 -5 0 5 10 15 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

alpha = 0.95, lambda = 2.25

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Figure 6. Quadratic utility function with parameters as shown in the inset.

2.6.4. Exponential utility function

One of the most popular prospect theory function is the exponential utility function (Camerer and Ho, 1994; Fishburn and Kochenberger, 1979).The function has the following form:

𝑈 𝑥 = 1 − e−𝑎𝑥 ; 𝑥 > 0

−λ + λe𝑎𝑥 ; 𝑥 < 0

Walker and Tversky(1993), Luce and Fishburn (1991) show that the form is applicable under reasonable condition, namely if preferences are invariant under an addition of a positive constant to outcomes. De Giorgi and Hens (2006) propose to use the exponential form instead of the power function, because of the boundaries of the exponential function. They argue that such boundaries in most cases are applicable in finance. However, other authors find some drawbacks of the form, such as it discourages the extreme risk because of higher curvature and large outcome of the function. In addition, its advantages such as persistence of boundaries can become disadvantage in some cases.

-6 -4 -2 0 2 4 6 8 10 12 14 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

alpha = 0.15, lambda = 2.25

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Figure 7. Exponential utility function with the parameters shown in the inset.

2.6.5. Selection of the function

The complete table of the functions and comments to the function are given below.

Table 1. The equations of the most popular prospect theory functions.

Function Equation Comments

Logarithmic ln α + 𝑥 ; α + 𝑥 > 0

λ ln(−(𝑎 + 𝑥)); α + 𝑥 < 0 Declining marginal utility.

Power x

α_{; 𝑥 > 0}

– λ(−x)α; 𝑥 < 0

Widely accepted in behavioral sciences.

Constant marginal utility.

Quadratic x − a𝑥2_{; 𝑥 > 0}

λ(x + a𝑥2_{); 𝑥 < 0}

Can be expressed in terms of means and variance.

Show inappropriate behavior for big values of arguments.

Exponential 1 − e

−𝑎𝑥_{; 𝑥 > 0}

−λ + λe𝑎𝑥_{; 𝑥 < 0}

Boundaries for the values of the function.

In general, the economic concept of a utility function represents a level of satisfaction by the consumption of the good. Utility function value is a base for decision making process of the participants in the market. Briefly, a person tends to make a positive decision when the utility function is higher and the level of desire for making the decision depends on the value of the

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

alpha = 0.67, lambda = 2.25

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function. Starting from rational theory of choice, the idea of utility function makes a significant evolution to modern behavioral theories. In this research, the idea that modern prospect theory utility can describe human behavior better than classical utility is proposed. The proposition is based on the empirical evidences and the findings of numerous researches.

The agents in this research consider the returns of commodity as the main motivation factor for buying or selling. Therefore, the utility function is used here as the measurement tool for forming their demand. The power utility function is chosen in this research because of the following reasons: the exponential function has boundaries which are not suitable in the case of price changes, the quadratic form has even more unrealistic behavior for price dynamics; the decreasing marginal utility of the logarithmic function is not a good choice for the reason which is similar to the exponential function.

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Chapter 3. The model developed in this research.

The model for this research has to include the chartists-fundamentalists market, a prospect theory utility function, as well as an impact of news. The section describes the model starting from chartist-fundamentalist model from section “Multi-agents models in stock market”.

The initial model is summarized in table 2 below.

Table 2. The summary of chartist-fundamentalist model.

Chartists price expectations

𝑝𝑡+1= 𝑝𝑡+ b M − 1(𝑝𝑡− 𝑝𝑀) + ζεt 𝑝𝑀 = 1 𝑀 𝑝𝑡−i 𝑀−1 𝑖=0

Fundamentalists price expectations 𝑝𝑡+1 = 𝑝𝑡+ γ(𝑝𝑓− 𝑝𝑡) + ζεt

Transitions probabilities 𝑃𝐶𝐹= β(1 + δ) K + NF N 𝑃𝐹𝐶 = β 1 − δ K + Nc N N = NF+ Nc

Price at the next period

𝑝𝑡+1= 𝑝𝑡+ ED + ζεt ED =NF N γ(𝑝𝑓− 𝑝𝑡) + Nc N( b M − 1𝑝𝑡− 1 𝑀 𝑝𝑡 −i 𝑀−1 𝑖=0 )

The first significant modification is an addition of the prospect theory utility into personality of agents. The agents create excess demands which can be seen from the function. In other words, the agents perceive information about price at the specific moment and create the demand proportionally to the value of the function. In the previous section, the power utility function has been chosen. The utility function adds behavioral properties and transfers part of the parameters of the model from the macro level to a micro level. In other words, the macro parameters b and γ are replaced by the parameters λ and α of the utility function. Therefore, the activity of the agents is described through the personal parameters instead of the macro parameters. The model applies the changes summarized in table 3.

Table 3. The behavioral improvements for the chartist-fundamentalist model.

Chartists price expectations 𝑝𝑡+1 = 𝑝𝑡+ U α, λ,

1

M − 1 𝑝𝑡− 𝑝𝑀 Fundamentalist price expectation 𝑝𝑡+1 = 𝑝𝑡+ U(α, λ, 𝑝𝑓− 𝑝𝑡)

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The news has an impact on the expectation of fundamentalists about the fundamental value. The items of news from Thomas Reuter analytics have several useful fields. The first one is sentiment divided by positive, negative and neutral with values from 0 to 1. The second one is relevance parameter with value from 0 to 1. The table 4 shows an example of the news data.

Table 4. Example of news data from Thomas Reuter. The given data describes the news elements

for different stocks for 1st of July 2014. The field IDN_TIME is date and time when the news occurred in the database. STOCK_RIC is a unique name of the stock. RELEVANCE is the power of relation of the news to the stock SENT_POS, SENT_NEUT and SENT_NEG represent the probabilities that the news is positive, neutral or negative. BCAST_TEXT is an automatically generated description of the news.

IDN_TIME STOCK_RIC RELEVANCE SENT_POS SENT_NEUT SENT_NEG BCAST_TEXT

01 JUL 2014 00:01:00.001 MTAL 0.258199 0.130286 0.123578 0.746136 Looming South Africa 01 JUL 2014 00:01:53.157 MTAL 0.5 0.294382 0.217224 0.488394 BRIEF-Black Star 01 JUL 2014 00:03:09.424 RUB 1 0.785923 0.0734177 0.140659 SHARES IN AUSTRALIA'S ANSE 01 JUL 2014 00:05:03.569 MTAL 1 0.109905 0.715185 0.17491 KINGSGATE CONSOLIDAT ED LTD 01 JUL 2014 00:05:20.205 MTAL 1 0.190274 0.559945 0.249781 KINGSGATE CONSOLIDAT ED

The neutral news is ignored, because it is assumed that they do not have impacts on the dynamics. Then the most likely number from negative or positive is selected depending on the results of comparison of the probabilities. Next the power of sentiment is calculated as: sentiment = SENT_POS, if SENT_POS > SENT_NEG

−SENT_NEG, if SENT_NEG > SENT_POS . The scaling multipliers are used for scaling impacts of relevance (RM) and sentiments (SM). The same procedure repeats for all news elements related to this time period t. As a result, the aggregate impact of news for the time period is taken into account by fundamentalists. The overall changes of fundamentalist function are described in table 5 below.

Table 5. The news improvements for fundamentalists.

Fundamentalist price expectation 𝑝𝑡+1= 𝑝𝑡+ U(α, λ, 𝑝𝑓− 𝑝𝑡+ ni=0sentiment𝑖 ∗ SM𝑖∗ relevancei∗ RM𝑖)

The formation of excess demand is similar to the base model except that the speed of the process of price is dynamic.

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Table 6 demonstrates the complete model for the research.

Table 6. The model developed in this research.

Chartists price expectations

𝑝𝑡+1= 𝑝𝑡+ U α, λ, 1 M − 1 𝑝𝑡− 𝑝𝑀 𝑝𝑀 = 1 𝑀 𝑝𝑡−i 𝑀−1 𝑖=0 Fundamentalists’ price

expectations 𝑝𝑡+1= 𝑝𝑡+ U(α, λ, 𝑝𝑓− 𝑝𝑡+ sentiment𝑖 ∗ SM𝑖∗ relevancei∗ RM𝑖

n i=0 ) Transitions probabilities 𝑃𝐶𝐹= β(1 + δ) K + NF N 𝑃𝐹𝐶 = β 1 − δ K + Nc N N = NF+ Nc

Price at the next period

𝑝𝑡+1= 𝑝𝑡+ Speed ∗ ED + ζεt

ED =NF

N U(α, λ, 𝑝𝑓− 𝑝𝑡+ sentiment𝑖 ∗ SM𝑖∗ relevancei∗ RM𝑖 n i=0 ) + Nc N U α, λ, 1 M − 1 𝑝𝑡− 𝑝𝑀

The dynamics of the model depends on the transition probabilities and a random term. In other words, these parameters add randomness to this model. The size of population equals to 500 and the parameter M equals to 50 for all experiments. Because of the purpose of simplification in most cases for the research the parameters 𝛃 and 𝛔 are set to zero. Therefore, in these cases the agents do not change their types and the uncertainty equals to zero.

The time step of the model depends on the specific case. For the cases in this model the time step equals to one day, the news data from the beginning of the day until the end of the day is aggregated for the expectations of next day’ price for the fundamentalists.

3.1. Calibration of the model

The calibration of the model is divided into two parts. The first part includes the calibration of the parameters for the behavior of an individual, namely, the loss aversion parameters of fundamentalists and chartists λfund, λchart and α. This study assumes that these parameters do not depend on the specific market. The last step of the estimation of the parameter has to be calculated for each market separately. The multipliers for sentiment and relevance as the speed of process of price changes are estimated. The scheme is shown in the figure below.

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Figure 8. Scheme of calibration.

Because the calibrations include several parameters, one of the heuristic schemes should be used. In this research a genetic algorithm is used as a heuristic algorithm for the estimation of the optimal parameters. The ideas of the evolution are the basis of genetic algorithms (Crosby, 1973; Fraser and Burnell, 1970). More precisely, a set of parameters or chromosome describes an organism. The fitness function is an average error calculated as a difference between predicted value and real value, when mutations and crossovers between the individuals are allowed. The mutations can appear with probability of 50% percent with 50/50 chance to change a parameter at 10% percent in both positive and negative direction. The crossovers happens with probability of 10% and assigns a value of the parameter as an average between values of this organism and an interbreed individual. Total population number equals to eight. The adjustment of the model held on period from the May, 1 of 2013 to the December, 31 of 2013.

The first round includes the two parts. Each organism for the first round has a chromosome (α, chartists risk aversion λchart , fundamentalist risk aversion λfund ).The news impact is not considered in the first round. The speed of the process of price dynamic equals to 1. The population of chartists equals to 250. Other parameters, namely, the transition probabilities and the noise are set to 0. In other words, the aim for this round is to estimate only the behavioral parameters for the agents. At the beginning, the genetic algorithm runs separately for four commodities, namely crude oil, wheat, gold and cotton. Next, the first and second individuals with the minimal value of the fitness function are chosen from all markets. Then, the

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combination of these two best fitted individuals from all the markets creates a new group which includes eight individuals for the last run. Finally, the genetic algorithm runs one for the last commodity market, namely coffee market. Each step of calculation takes 100000 iterations for each market, 500000 totally. The result of the estimation is given in table 7 below.

In this thesis, the absolute error for a simulation at time t is an absolute difference between the prices for the commodity 𝑅𝑒𝑎𝑙𝑃𝑟𝑖𝑐𝑒 𝑡 and the predicted price 𝑃𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑𝑃𝑟𝑖𝑐𝑒 𝑡

𝜀_𝑡𝑎𝑏𝑠 = |𝑃𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑𝑃𝑟𝑖𝑐𝑒 𝑡 − 𝑅𝑒𝑎𝑙𝑃𝑟𝑖𝑐𝑒 𝑡 | .

The relative error is 𝜀_𝑡𝑟𝑒𝑙 ₌|𝑃𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑𝑃𝑟𝑖𝑐𝑒 𝑡 − 𝑅𝑒𝑎𝑙𝑃𝑟𝑖𝑐𝑒 𝑡 |

𝑅𝑒𝑎𝑙𝑃𝑟𝑖𝑐𝑒 (𝑡) ∗ 100%.

Table 7. Results of behavioral parameters estimation in the last calibrations. The table includes

the loss averse 𝛼 and risk parameters for chartists 𝜆_{𝑐ℎ𝑎𝑟𝑡} and fundamentalists 𝜆_{𝑓𝑢𝑛𝑑}. The

average absolute error is an average difference between predicted values and real values for these parameters, the relative error is an average value of the differences between predicted values and real values divided by the real value.

Loss averse(𝛂) Chartist Risks(𝛌𝐜𝐡𝐚𝐫𝐭) Fundamentalist Risk(𝛌𝐟𝐮𝐧𝐝) Average absolute error ( 𝝁_𝜺𝒂𝒃𝒔) Average relative error ( 𝝁_𝜺𝒓𝒆𝒍) 0,67 2,52 2,01 136,13 10,13% 0,94 4,00 1,88 139,51 10,38% 0,85 2,11 1,56 142,30 10,58% 0,78 2,95 1,06 142,85 10,63% 0,65 9,35 8,00 143,00 10,64% 0,97 12,50 7,00 143,66 10,69% 0,76 2,64 1,17 143,74 10,69%

The dispersion of the results is relatively small, but the most optimal results correspond to the individual with λ_fund = 2.012, λ_chart = 2.523 and α = 0.6743. The second reason to choose this results compared to the second one is the smaller difference between risk averse of chartists and fundamentalists. In this research it is proposed that losses harm chartists slightly more than fundamentalists, because the fundamentalists think that they know the real price for the commodity and thus they believe that prices of the stock will converge to a fundamental value. The estimated values are used in all experiments in this research.

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The second step of the calibration depends on the chosen market. The results of the model are demonstrated on three markets: crude oil, cotton and gold. The calibration takes 50000 iterations for each market. The best results for each market are showed in table 8.

Table 8. Results of the estimation of the parameters of news and market for gold, crude oil and

cotton. The table includes the name of commodity, the speed of the price dynamic process, the sentiment and relevance multiplier and the average absolute and relative error for corresponded parameters.

Commodity Speed SM RM ChartistNum 𝝁_𝜺𝒂𝒃𝒔 𝝁_𝜺𝒓𝒆𝒍

Gold 2.3 2.04 9.03 50 18.67 1.42%

Crude Oil 1.6 2.3 6.9 113 3.7 2.97%

Cotton 1.9 7.32 3.04 120 5.31 5.9%

The average relative error for the model with news and market parameters and without these parameters shows that the quality of the prediction differs significantly. The graph below gives an illustration of the differences for gold. The parameters in the illustration match the parameters from tables 7 and 8. The main observed feature is that the news factor gives the opportunities for both better quality of prediction and the predictions of the dynamics of fluctuations.

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Figure 9. The first plot shows the simulation for the model for gold with the behavior parameters

only and the second demonstrates the simulation with the behavior, news and market parameters. The period for both plots is from the January, 1 of 2014 to August, 29 of 2014. For both cases, the calibrated parameters are used. ,

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The calibrated parameters are calculated through the heuristic algorithm and therefore the parameters are not optimal. In spite of this, the aims of the calibration are still to find the value of parameters which are sufficient enough as well as find the values for the minimal time. Therefore, an empirical analysis of the results satisfies the aims. The two important elements of a genetic algorithm are the number of generations and the population size. The numbers of generations in this research are set to 50000 and 100000 for different kinds of estimates due to the fact that these numbers are high enough to produce accurate estimation and it is not too difficult to finish the estimation within a reasonable period. Because both the number of generations and population size cannot be set to sufficient big value, the population size is the milestone of genetic algorithms for the research. Despite that the small size of a population can lead to poor solutions (Pelikan et al., 2000) in practice, the difference between the best results of the fitness function for 5 and for 200 chromosomes can be less than 10% (Roeva et al., 2012). For the calibration, we confirm that the changes are not significant in case of the model. The final calibration of the behavior parameters for the coffee market is repeated for a different size of population. The results in table below show that the bigger population does not deliver better numbers, with one exception when the fundamentalists take much more risks than chartists, which is not acceptable by the assumptions. As a result, the empirical evidence gives sufficient basis for using 8 chromosomes for the calibration.

Table 9. Results of the estimation of the behavior parameters for the coffee market for different

size of the population. There is no significant increasing of the quality of prediction with increasing of the size of population.

Population size 𝝁_𝜺𝒂𝒃𝒔 𝛂 𝛌_{𝐜𝐡𝐚𝐫𝐭} 𝛌_{𝐟𝐮𝐧𝐝}

16 143 0.79 2.34 2.11

24 137.83 0.91 0.08 0.04

32 132.24 0.82 15.61 3.3

64 135.7 0.74 51.17 1.42

On the whole, the model reveals significant ability to learn and shows good results of the learning for almost all markets. The calibration of the model allows the applications of the model for the practical purposes, namely for predicting the price dynamics for different markets. The examples for work of trained model and statistical data for the examples are demonstrated in the next section.

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Chapter 4. Results

This section includes examples of simulations with different parameters for three commodities: gold, crude oil, cotton. The price data for the modeling is collected from the historical database of Investing.com. The data covers period from January, 1 of 2014 to July, 3 of 2014.

Fundamental value for the commodities is collected from Rabobank Forecasts. These forecasts are monthly predictions from analysts for different commodity stocks. Moreover, the forecasts include assumptions about price for several following quarters and analysis of reasons for the movements of the fundamental values. The forecasts of fundamental values and the price are included in the appendices.

The following subsection demonstrates the behavior of the model for the commodities. The section includes a primary analysis based on assumptions about significant events and the properties of human perceptions. In addition, it gives a visual presentation of the changes in the behavior of the model according to the changes of the parameters.

Next, the tests of robustness for the model are given. This subsection includes a measure of the sensitivity for different parameters of the model. These results show that the sensitivity of the model reacts on the different parameters in an irregular way. On the whole the results show that the model is robust against all parameter changes.

The last subsection in this chapter describes the limitations of the model. This part gives the challenges, difficulties and boundaries of the model.

4.1. The examples of implementation for different commodity stocks

This section depicts the results of simulations of this model for the several commodities.

Each case contains a set of plots with different parameters, statistics of the accuracy of the simulation and a brief analysis of the demonstrated behavior. The plots start from January, 1 of 2014 and contain the dynamics for real price of the commodity, predicted price of commodity and fundamental value of the commodity. The X- axis is enumerated in days and Y – axis is enumerated in unit of currency per unit of the good depending on the market where the commodity is traded. For all these graphs the real calculation starts from day number 10, because the period before is used for adjustment of the chartists behavior.

The second graphs show the distribution of relative errors for the case. Specifically, the relative error is calculated for all time points. The relative error is the difference between predicted and

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real price divided by real price. Next, the whole data is divided into ten segments starting from minimum value of deviation to maximum. Last, the frequencies of the relative error are calculated for each segment and the probabilities for the segments are displayed in the graphs. The X – axis is enumerated in the currency per unit. The Y – axis represents probability and the Y-axis is enumerated in numbers from 0 to 1.

All tables in this section contain an average price 𝜇𝑅𝑒𝑎𝑙𝑃𝑟𝑖𝑐𝑒 , an average absolute error 𝜇𝜀𝑎𝑏𝑠, a standard deviation of the absolute error 𝜎_𝜀𝑎𝑏𝑠, an average relative error 𝜇_𝜀𝑟𝑒𝑙 and a standard

deviation of the relative error 𝜎_𝜀𝑟𝑒𝑙. The bold row represents the results for calibrated parameters,

the rest of the table gives results when all parameters are calibrated except one. This uncalibrated parameter differs for each commodity, namely the sentiment multiplier for gold, the sigma for crude oil and the number of chartists for cotton.

One of these plots demonstrates the result with calibrated parameters, the other plots show changes in the results relating to the changes in selected parameters. The plots create sufficient basis of intuition for the better perception of robustness of the model given in the next section.

In addition, the section with results for gold gives the results for different utility function and provides brief explanation of the behavior.

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4.1.1. Gold

The graphs exhibit dynamics for gold in the USA dollars per Troy Ounce. The best prediction results are showed in the first plot with the sentiment multiplier equals to 2.04. The simulation shows that the trained model predicts the price dynamics with a good level of quality. All parameters for the simulation are fixed except the sentiment multiplier. The changes in sentiment multiplier show that sharpness of the graph strongly relates to the multiplier.

Table 10. Accuracy statistic for gold. The results for calibrated parameters (Speed = 2.3, SM =

2.04, RM =9.03, ChartistsNum = 50) are shown in the first row.

Gold 𝝁𝑹𝒆𝒂𝒍𝑷𝒓𝒊𝒄𝒆 𝝁𝜺𝒂𝒃𝒔 𝝈_𝜺𝒂𝒃𝒔 𝝁_𝜺𝒓𝒆𝒍 𝝈_𝜺𝒓𝒆𝒍

SentimentMultiplier=2.04 1294.48 15.37 12.46 1% 1%

SentimentMultiplier =6.04 1294.48 22.27 14.93 2% 1%

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Figure 10. The prices of gold and the corresponded distributions of the relative errors. First

graphs give comparisons between the real price (yellow line) and the predicted price (green line). The results for calibrated parameters (Speed = 2.3, SM = 2.04, RM =9.03, ChartistsNum = 50) are shown in the plot №1.The figures of SM are 2.04, 6.04 and 11.04 respectively.

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The last four graphs illustrate the differences between utility function for the dynamics of the model. The demonstration shows the usage of four utility functions for gold. The results explain that the choice of the function is extremely important, because the behavior of the model differs completely for different functions.

The logarithmic function has the property of declining marginal utility and thus the news has little impact on the model. The exponential function shows calm and almost static behavior, because the value of the functions is bounded and thus the changes in demand are bounded. The most unrealistic result shows in the quadratic function because it is not always positive when price is positive and it is not always negative in the negative region. The quadratic function follows the fundamental value. It happens because the calibrated parameter 𝛼 equals to 0.02 what almost removes the dynamic for the model. The parameters obtained during calibration procedure for coffee are used for all the functions. The calibrated parameters for each function, the relative errors and deviations are given in table 11 below.

Figure 11. The comparisons between the real price (yellow line) and the predicted price (green

line) for different utility functions. The upper left plot uses power utility, the upper right shows the results for exponential function, the bottom left plot presents the results for logarithmic utility and the bottom right shows the quadratic utility function.

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Table 11. Calibrated parameters and the relative errors for different utility functions.

On the whole, the power utility function shows the most appropriate behavior for the model.

Function 𝛂 𝛌𝐜𝐡𝐚𝐫𝐭 𝛌𝐟𝐮𝐧𝐝 𝝁𝜺𝒓𝒆𝒍(𝝈_𝜺𝒓𝒆𝒍) SM RM Speed

Power 0.67 2.52 2.01 1%(1%) 2.04 9.03 2.3

Logarithmic 0.47 1.50 1.30 2%(1.8%) 2.71 8.86 0.85

Exponential 0.63 2.19 1.91 3.4%(2%) 0.91 2.38 3.24

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4.1.2. Crude Oil

The price for the commodity is given in US$ per one barrel. The main specific for the dynamic simulation is a strong difference between behavioral of the model for all available news and for the alerts. An alert is a short message with information related to the commodity. The figures show difference between reaction to all available information and to the alerts only. Figure 11 and first plot in figure 12 demonstrate that participants react mostly on quick messages about the commodity. It is assumed that because of high volatility of the oil stock and because of speculative nature of crude oil dynamic (Engdahl, 2008) the participants trust in the short term news much more than in the long term predictions.

In addition, the two last graphs in figure 12 show impacts of stochastic variables to the behavior. The both of the simulation runs with sigma equals to 1. The graphs reveal that the stochastic parameters can change prediction behavior significantly. Thus, it is an illustration of motivation to reduce the usage of the stochastic parameters in predictions for the research.

Table 12. Accuracy statistic for crude oil. The results for calibrated parameters (Speed = 1.6,

SM = 2.3, RM =6.9, ChartistsNum = 113) are shown in the second row.

Crude Oil 𝝁𝑹𝒆𝒂𝒍𝑷𝒓𝒊𝒄𝒆 𝝁𝜺𝒂𝒃𝒔 𝝈𝜺𝒂𝒃𝒔 𝝁𝜺𝒓𝒆𝒍 𝝈𝜺𝒓𝒆𝒍

FullNews.Sigma = 0 100.82 32.86 8.24 32% 8%

Alert.Sigma = 0 100.82 2.91 1.91 2% 1%

Alert.№1 Sigma = 1 100.82 16.31 11.73 16% 12%

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Figure 12. The prices of crude oil and the corresponded distribution of the relative errors. First

graph is a comparison between the real price (yellow line) and the predicted price (green line) for full news data. The results are given for calibrated parameters (Speed = 1.6, SM = 2.3, RM =6.9, ChartistsNum = 113) For the figure sigma equals to 0.

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Figure 13. The prices of crude oil and the corresponded distribution of the relative errors. First

graphs give comparisons between the real price (yellow line) and the predicted price (green line) for alerts. The results for calibrated parameters (Speed = 1.6, SM = 2.3, RM =6.9, ChartistsNum = 113) are shown in the plot №1. For the figure sigma equal 0, 1 and 1 respectively.

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4.1.3. Cotton

The graphs contain information about cotton stock for the period. The unit of measurement for this stock is US$ per one pound. There is a significant impact of proportion of chartist on behavior of the model. Visually, the bigger proportion of chartists means that changes in price are much more dynamic compared to the case with lower proportion of chartists. In addition, the chartists create bubbles in the commodity price dynamic. The creation of the bubbles is a well-known property of the model. The model reveals the most accurate estimation when population of chartists equals to 120 with total population equals to 500.

At first glance, the model exhibits inappropriate behavior for the commodity and the prediction is performed with insufficient accuracy. In fact, the price in the period from day 110 to 130 reveals excellent results. Thus the news has an impact on the dynamic, but the impact is revealed with time delay. It is assumed that the proposition for this behavior is a limited attention as was shown in the section “Perception of the news”. From this perspective the dynamic of the prediction can be explained through the delay in perception of the new information. More precisely, in contrast to efficient market hypothesis, the delay can be equal to several months.

Table 13. Accuracy statistic for cotton. The results for calibrated parameters (Speed = 1.9, SM

= 7.31, RM =3.04, ChartistsNum = 120) are shown in the first row.

Cotton 𝝁_{𝑹𝒆𝒂𝒍𝑷𝒓𝒊𝒄𝒆} 𝝁_𝜺𝒂𝒃𝒔 𝝈_𝜺𝒂𝒃𝒔 𝝁_𝜺𝒓𝒆𝒍 𝝈_𝜺𝒓𝒆𝒍

ChartistNumber = 120 87.89 19.28 10.07 21% 11%

ChartistNumber = 200 87.89 31.03 15.46 35% 17% ChartistNumber = 320 87.89 29.96 15.32 33% 16% ChartistNumber = 420 87.89 25.78 14.63 29% 16%

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Figure 14. The prices of cotton and the corresponded distributions of the relative errors. First

graphs give comparisons between the real price (yellow line) and the predicted price (green line). The results for calibrated parameters (Speed = 1.9, SM = 7.31, RM =3.04, ChartistsNum = 120) are shown in the plot №1. For the figure ChartistsNum equals to 120,200,320,420 respectively.

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News and Behavioral Impact on Commodity Markets through Multi-Agent Modeling