Users Manual for 8.1.02-05
Contents
1. Euler algorithm each manager is assumed to move horizontally up the slope of the payoff function by the substep increment u jump stepsize u slope This increment is clipped to a maximum size set by a slider max u jump With every step Cor u step substeps there is also a vertical motion due to increment or decrement of the size of the manager s portfolio due to payoffs The slope of the Landscape or gradient of phi phisubx is shown in color ona row in the center of the graphics window Here is the color code red for positive slopes Cmove to the right green for negative slopes move to the left and yellow for a narrow zone around zero HOW TO USE IT STEP 1 SET THE INITIAL HERD Add Managers Panel Cla Set the population slider to determine the number of managers in the initial herd 1b Set the center slider to locate the horizontal center of the initial herd Horizontal axis corresponds to strategy choice 1c Set the width slider to determine the horizontal width of the initial herd as a percentage of the total horizontal width of the window 1d Set the altitude slider to Locate the vertical center of the initial herd Vertical axis corresponds to initial portfolio size Cle Set the height slider to determine the vertical width of the initial herd as a percentage of the total vertical width of the window C1f Press the setup button to create the initial distribution of managers The initial histo2. to a higher value of c2 lets say 7 how do they react now The frequency choice drop down also plays an important role for determining how the simulation proceeds After picking values for your risk cost c2 choose different values of time by adjusting the drop down notice the different speeds of convergence or divergence Play with different groupings of managers by selecting different values for center width population etc Try creating a group of managers at different ends of the veiw window Maybe a puff at center 20 and another at center 80 How does this affect the outcome How does a weighted group balance with a lighter one one group with higher population compared to a smaller one Finally the values for max u jump and climbrate will help you to avoid or control numerical artifacts If the setting you choose create Large spikes in the the behavior of your managers it may be a good idea to lower your climbrate and then adjust your max u jump to help reduce or eliminate these types of swings You can also try setting your model out from the beginning with a very Low climbrate and max u jump and see how your simulation reacts THINGS TO NOTICE Notice the Landscape view window and watch how the steepness or shallowness of your selection changes the behavior of your managers How does the c2 slider affect this dynamic How about the influence of time frequency and the climbrate Also notice h
3. Market Model 8 1 Users Manual by Ralph Abraham Revised 09 January 2007 WHAT IS IT User s Manual for NetLogo Market Model 8 1 rev 5b of 31 December 2006 by Ralph Abraham and Dan Friedman This manual is devoted primarily to the Graphical User Interface of the model The NetLogo code under the Procedures tab is explained in another document the Program Guide This is the first extension of a NetLogo model for financial markets It implements two innovations surprise stochastic variations in payoff and the c2 dynamic varying the c2 coefficient in the gradient rule Further background may be found at www vismath org research Landscapedyn models market HOW IT WORKS The turtles represent money market managers Each manager is shown as a small triangle in the graphics window They have different colors just for the visual effect When several are on the same patch discretized interval of the strategy space only the top one can be seen in entirety but the x and y positions are floating point numbers so parts of lower turtles may be seen The state space is shown as the upper half of the graphics window The horizontal axis represents a unit interval corresponding to the choice of strategy u This is the degree to which the manager is willing to invest in risky assets Moving to the right increases risk The vertical axis represents the value of the manager s portfolio Zero is indicated by the horizontal magenta strip in the center
4. a new run or press init datafile if you want to continue the current run In either case a file time series txt is opened in the current directory with a header showing the parameters of the current run It a file times series txt already exists it will be appended with a new header Header data includes time and date frequency u steps totalpop center width altitude height gs1 RO dR sigma tau beta eta W and T Time series data includes totalsteps totaltime DPM R1 c2 mean Lhat and crash detected The latter is one if the minimum price divided by maximum price Cin the time window of length W steps is less than T Both W and T are set by sliders STEP 3 ACTION Top row of buttons 3a Press setup to begin a simulation 3b Press the step button to activate a single step in the market game Every manager will take one step horizontally in proportion to the slope of the Landscape at its current position Cthe value of phisubx at its current u and vertically in proportion to its value in the payoff function You will see the managers move and then the histogram will be redrawn Press step several times to judge the stepsize choice and the jitter in the position of the maximum indicated by the yellow zone in the color bar After ten clicks the plots will be refreshed 3c Press go to trigger a rapid sequence of steps Press go again to halt the action 3d Press subst
5. ep to monitor the effect of a single substep 3e Press show jiggle to display the effect of jiggle 3e While action is stopped press do math to update most variables in case some sliders have been changed without actually taking a step of the simulation 3e Press restore to reset sliders to default values 3f Press rewind1 while simulation os on pause to restore all variables to the preceding step 3g Press rewind2 to go back two steps THE GRAPHICS WINDOW The Mean Queen a large white circle in the Graphics Window indicates the position Cmean u mean z The Yellow King is a yellow triangle just above the slope color bar It s horizontal position shows the value of the cluster point u see page 8 of B C Eventually if the herd converges to a cluster u will be at the maximimum of phi and zero of phisubx and thus the yellow king will be within the yellow bar The cluster point u is the solution of an algebraic equation derived from slope 0 under the assumptions A uLi mean u all i Cthat is a cluster and B mean u dot that is the cluster is at a critical point To solve the equation we have used an approximation obtained numerically by Newton s method THE PLOTS With each ten steps the plots are redrawn Density of managers vs u essentially a histogram Landscape phi vs u PM price of the risky asset vs step number a tickertape display At present the density p
6. gram shows the initial distribution STEP 2 SET THE RUNTIME PARAMETERS C Runtime Dashboard 2a Adjust the frequency chooser for the desired number of steps per year 2b Adjust the u steps chooser for the desired number of substeps per step 2c A slider called yellow width adjusts the width of the yellow band in the color bar which shows where the slope is in the u interval C yellow width yelLow width SO if the yellow bar is too wide just A stop with a press on the GO button B reduce this yellow width slider C press STEP once to see if new value is OK D press GO again OR simply adjust the slider during a run 2d Adjust the Loss redline slider to reveal the local losses Lhat of the managers 2e Change turtle size at any time for visibility of managers turtles C2f g h Experiment with different values of gs1 RO and dR Cnote Rs RO dR 2i j Experiment with the sliders for sigma and tau to control the 0 U process for surprise The button show jiggle indicates the magnitude of the surprise process 2k The alpha slider controls the exponent in the price formula B C 4 21 The beta slider controls the magnitude of the c2 dynamic as c2 beta mean Lhat 2m n Experiment with the eta slider to control the strength of the local loss memories Lhat WRITE DATA section To save time series data to a file set write data switch to on Then press setup to start
7. lot is only approximate THE MONITORS to the right of the plots After each step the monitors are updated showing z min totalpop mean u and mean z same as the mean queen and mean u dot DPM the detrended price of the risky assets RO Rs and R1 multiplier of u term in phi totalsteps totaltime based on number of steps and lcoaltime based on number of substeps stepsize and stepsize u The zmin monitor shows the fixed zmin of the model which occurs in the center of the graphics window The zmax slider allows the upper Limit of the z scale to be set between and 10 This is an absolute maximum for the portfolio worth of any manager and should be a positive integer After changing this slider one must click setup and begin a fresh run DIAGNOSTICS Below the Landscape plot is a pair of diagnostic tools created by Pablo Viotti These can be switched on and off and track the attributes of interesting managers THINGS TO TRY Begin by using the default startup settings with c2 Frequency and zmax The sliders for max u jump and climbrate will be adjusted Later as well Push the setup button and then press the go button How do the managers react and how long does it take to reach a stable position Now while still running the simulation adjust your c2 slider to a Lower number lets say 3 to adjust for a different risk cost or risk premium How do the managers react Now move your slider again
8. of the graphics window The upper Limit is set by a slider the default value is four A portfolio value of one is normal A chosen number of managers begin at initial positions in the state space Model coordinates u z correspond to screen coordinates xcor ycor The initial distribution is important to the outcome of a run The model starts up with a random distribution in a rectangle of setable width sliders for width and center and height Csliders for altitude and height At the start and after each step of the run the density of managers as a function of the horizontal coordinate in the strategy space is shown as a histogram in the plot window The stepsize may be set with the frequency chooser drop down menu For example if 52 is chosen in the drop down menu this signifies a frequency of 52 steps per year weeks and the variable stepsize in the program is set to 1 52 years An additional parameter u steps may be set with a chooser This is the number of substeps in a step Increasing u steps decreases the substepsize called stepsize u to stepsize u steps and decreases the numerical error in the Euler integration of the hill climbing process The speed of the simulation is slower of course That is stepsize is a unit of time for periodic reports of financial data including z updates while stepsize u is the increment for the Euler steps of the gradient dynamics of strategy adjustment or updates of u Using the
9. ow the yellow triangle behaves where does the simulation expect our managers to go Also notice the risky price or yeild that your model may or may not stabalize around does it go up or does it go down with a specific selection Watch the behavior of your managers given different time frequencies when you change your climbrate CREDITS AND REFERENCES Many thanks to Uri Wilensky for his cleverness and industry and to the NSF for support in the creation and evolution of the NetLogo system Also we thank Pablo Viotti for help with the model code and Matt Draper and Don Carlisle for assistance with the docs
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