Three Different Ways Synchronization Can Cause Contagion in Financial Markets

We introduce tools to capture the dynamics of three different pathways, in which the synchronization of human decision-making could lead to turbulent periods and contagion phenomena in financial markets. The first pathway is caused when stock market indices, seen as a set of coupled integrate-and-fire oscillators, synchronize in frequency. The integrate-and-fire dynamics happens due to change blindness, a trait in human decision-making where people have the tendency to ignore small changes, but take action when a large change happens. The second pathway happens due to feedback mechanisms between market performance and the use of certain (decoupled) trading strategies. The third pathway occurs through the effects of communication and its impact on human decision-making. A model is introduced in which financial market performance has an impact on decision-making through communication between people. Conversely, the sentiment created via communication has an impact on financial market performance. The methodologies used are: agent based modeling, models of integrate-and-fire oscillators, and communication models of human decision-making


26
Financial markets are generally thought of as random and noisy, beyond an understanding 27 within an ordered framework. The elusive nature of the markets has been captured in theories like 28 the efficient market hypothesis, basically considering price movements as random. Behind such a 29 notion is the idea that price movements happening on a given day is a random phenomenon, 30 basically taken from some probability distribution, describing in probabilistic terms what kind of 31 event one should expect happening on a given day. The assumption seems natural and probably 32 has its roots back in time, when people working in finance at the beginning of a work day, would 33 turn on their radio, and register new financial events (again, the events assumed to be created by 34 some higher instances). Such a descriptive framework also holds for more modern and general 35 schema used in Finance, such as ARCH and GARCH models which are able to describe many of the 36 stylized facts observed in empirical data. Socio---Finance [1] instead try to emphasize non---random 37 human impact in the formation of prices in financial markets, in particular stressing the interaction 38 taking place between people, either directly through communication or indirectly through the 39 formation of asset prices which in turn will be seen to enable synchronization in decision making.

40
Documents de travail du Centre d'Economie de la Sorbonne -2017.59 Synchronization in human decision making, and the impact it could have on financial asset price formation, is not a well understood topic. The term is more known in economics, where empirical studies have shown that international trade partners display synchronization in business 44 cycles. Dées and Zorell [2] find that economic integration fosters business cycle synchronization 45 across countries. Also similar production structure is found to enhance business cycle co---46 movement. By contrast, they find it more difficult pinpoint a direct relationship between bilateral financial linkages and output correlation. For other references that studies the topic of

58
It should be noted that the term "synchronization" in this article covers a broader phenomenon 59 than "herding", a related term often used in the financial literature. In finance "herding" usually 60 refers to the simple case where people intentionally copy the behavior of others. It has been 61 suggested that it is rational to herd [9]. For instance; portfolio managers may mimic the actions of 62 other portfolio managers just in order to preserve reputation. It is easier to explain an eventuality 63 failure when everybody else also fails, than expose a failure due to bold forecasts and deviation 64 from the consensus. For a general review paper on herding see [10] hedging policy, and fund managers would prefer the unregulated case with high maximum 77 leverage. Aymanns and Georg [8] instead consider the case when banks choose similar investment 78 strategies, which in turn can make the financial system more vulnerable to common shocks. They 79 consider a simple financial system in which banks decide about their investment strategy based on 80 a private belief about the state of the world, and a social belief formed from observing the actions of 81 peers. They show how the probability that banks will synchronize their investment strategies 82 depends on the weighting between private and social belief.

84
In the following we will place the emphasis on the fact that price formation is the result of       down. It should now be noted that whatever the price movement at the next time period t+1, the 142 strategy in table 1 will always predict to sell at time period t+2. Therefore we don't need to wait for 143 the market outcome at the next time step t+1 in order to know what the strategy will suggest 144 following that time step: it will always suggest selling at time t+2. That such kinds of dynamics in 145 the decision making of technical analysis strategies could be relevant for real market was suggested 146 in [15]. In the terminology of [15] the strategy in table 1 is called "one time step decoupled 147 conditioned on the price history = (010) " and denoted ! !"#$%&'"! ( ).
(i.e. conditioned on knowing ( ) one cannot know the prediction of ! !"#$%&' ( ) at time t+2 before 150 knowing ( + 1)), and those decoupled to the price history. Considering only the strategies 151 actually used by the agents to trade at time t, the order imbalance, A(t), can therefore be written: In expression (3) ! (t) is the return of stock index j, which at time t receives a contribution from 245 stock index j, whenever the "stress" !" !"# exceeds a certain threshold ! . !" describes the coupling 246 between the two stock indices, expressed via (5) in terms of the relative weight of capitalizations ! .

255
It is seen from (4), that it is the tensor !" !"# , that places the role of an IAF oscillator. Returns from 256 index j, ! , accumulates stress on index i by continuously adding to !" !"# , up to a certain point,

257
!" !"# > ! , after which the oscillator discharges, !" !"# → 0, and the stress becomes priced---in via Once the IAF network is in a state of synchronization, it is possible to identify contagion effects throughout the network. One example is given in Figure 5

283
To see how this can take place consider Figure  6.a below, which illustrate a population of market 284 participants with different views of the market, which we for simplicity will take either to be 285 positive, bullish, or negative, bearish.

302
In the context of decision making with respect to trading assets in financial markets, it is natural to 303 assume that the market performance itself could influence the decision making of the market 304 participants, whereas this in turn could influence future market performance. In order to capture 305 such kinds of feedbacks, a model was suggested in [25]. The main idea is to let the market 306 performance influence the decision making, instead of the simple majority rule seen in Figure  6.b---c.

320
It should be noted that the transition probabilities , (t) depend on time, since we assume that they 321 change as the market performance changes.

322
The link between communication and its impact on the markets, can now be taken into account by 323 assuming that the price return r(t) changes whenever there is a change in the bullishness. It should 324 now be noted, that it is the changes in opinion that matters for the market performance, rather than 325 the level of a given opinion. Empirical data supporting this idea, can for example be found in [26].

326
The reasoning behind this, is that people having a positive view of the market would naturally 327 already hold long positions on the market. It is therefore rather when people change their opinion,

328
say becoming more negative about the market, or less bullish, that they will have the tendency to Here ( ) is a Gaussian distributed variable with mean 0 that described a standard deviation that 333 varies as a function of time depending on changes in sentiment: The impact from the market performance on the decision making, can then be taking into account