breed [uninformed] breed [informed] uninformed-own [endowment] informed-own [endowment] globals [i x y ;;;;; variables used for setting banks totalEU ;;;;; total endowment of uninformed totalEI ;;;;; total endowment of informed AFprice Mprice ;;;;; AFprice = arbitrage-free price Mprice = market price #-of-transactions base ;;;;; base for the price shock] ;;;;;;;;;;;;; ;;; SETUP ;;; ;;;;;;;;;;;;; to setup clear-all setup-banks setup-uninformed setup-informed setup-prices do-plots end ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; to setup-banks set i 0 while [i < #-of-banks] [extraction] end to extraction ifelse random 100 < 50 [set x random 12][set x (-(random 12))] ifelse random 100 < 50 [set y random 12][set y (-(random 12))] ask patches with [pxcor = x and pycor = y][ifelse pcolor = 0 [set pcolor 66] ;;;;; 66 = light green [extraction set i i - 1]] set i i + 1 end ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; to setup-prices set base 10 set AFprice base set Mprice random-normal base 1 if Mprice < 0.1 [set Mprice 0.1] end ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; to setup-uninformed create-uninformed #-of-agents * (1 - (%-of-informed / 100)) ask uninformed [setxy random-xcor random-ycor set shape "person" set color grey ifelse random 100 < %-of-rich-agents [set endowment rich-endowment] [set endowment poor-endowment]] ask uninformed [set totalEU totalEU + endowment] end to setup-informed create-informed #-of-agents * (%-of-informed / 100) ask informed [setxy random-xcor random-ycor set shape "person" set color red ifelse random 100 < %-of-rich-agents [set endowment rich-endowment] [set endowment poor-endowment]] ask informed [set totalEI totalEI + endowment] end ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;; ;;; GO ;;; ;;;;;;;;;; to GO if not any? uninformed [if not any? informed [stop ]] tick AFprice-dynamic move-agents uninformed-dynamic informed-dynamic do-plots end ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; to AFprice-dynamic set shock 0 if random-normal 0 1 > 2.16 ;;;;; probability 1.54% [set shock (random-normal 0 1)] if base + shock + sin ticks < 0.1 ;;;;; 0.1 is the lower bound of the AFprice [set shock 0.1 - (base + sin ticks)] set base base + shock set AFprice base + sin ticks end ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; to move-agents ask uninformed [right random 360 forward 1] ask informed [right random 360 forward 1] end ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; to uninformed-dynamic ask uninformed [if endowment <= 0.1 [die]] ask uninformed [if pcolor = 66 [transaction-uninformed]] end to informed-dynamic ask informed [if endowment <= 0.1 [die]] ask informed [if pcolor = 66 [ if Mprice != AFprice [transaction-informed]]] ;;;;; != means it "is not egual to" end ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; to transaction-uninformed set totalEU 0 ifelse random-normal 0 1 < 0 [if Mprice > (0.1 * AFprice) ;;;;; Mprice can't be < of -90% AFprice [ifelse sales-not-available? [if random 100 > Pr-sales-not-available [sell]] [sell]]] [if Mprice < (1.9 * AFprice) ;;;;; Mprice can't be > of 90% AFprice [ifelse purchases-not-available? [if random 100 > Pr-purchases-not-available [buy]] [buy]]] ask uninformed [set totalEU totalEU + endowment] converge end ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; to transaction-informed set totalEI 0 ifelse Mprice > AFprice ;;;;; SELL [ifelse sales-not-available? [if random 100 > Pr-sales-not-available [sell]] [sell]] ;;;;; BUY [ifelse purchases-not-available? [if random 100 > Pr-purchases-not-available [buy]] [buy]] ask informed [set totalEI totalEI + endowment] converge end to sell set #-of-transactions #-of-transactions + 1 set endowment (endowment + (0.01 * (Mprice - AFprice) * endowment)) ifelse (Mprice - (0.0001 * endowment)) > (0.1 * AFprice) [set Mprice (Mprice - (0.0001 * endowment))] [set Mprice (0.1 * AFprice)] end to buy set #-of-transactions #-of-transactions + 1 set endowment (endowment - (0.01 * (Mprice - AFprice) * endowment)) ifelse (Mprice + (0.0001 * endowment)) < (1.9 * AFprice) [set Mprice (Mprice + (0.0001 * endowment))] [set Mprice (1.9 * AFprice)] end to converge if abs (Mprice - AFprice) < 0.01 * AFprice ;;;;; abs = absolute value [set Mprice Afprice] end ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;;;;; ;;; GRAPH ;;; ;;;;;;;;;;;;; to do-plots set-current-plot "Prices" set-current-plot-pen "AFprice" plot AFprice set-current-plot-pen "Mprice" plot Mprice end @#$#@#$#@ GRAPHICS-WINDOW 590 10 1060 501 11 11 20.0 1 20 1 1 1 0 1 1 1 -11 11 -11 11 0 0 1 ticks CC-WINDOW 5 515 1069 610 Command Center 0 BUTTON 10 10 98 50 Setup Setup NIL 1 T OBSERVER NIL S NIL NIL SLIDER 224 10 385 43 #-of-banks #-of-banks 5 50 45 5 1 NIL HORIZONTAL SLIDER 223 75 383 108 #-of-agents #-of-agents 10 100 80 5 1 NIL HORIZONTAL MONITOR 107 10 217 55 Arbitrage-Free Price AFprice 2 1 11 BUTTON 10 50 98 90 GO GO T 1 T OBSERVER NIL G NIL NIL PLOT 10 248 582 500 Prices NIL NIL 0.0 10.0 5.0 15.0 true true PENS "AFprice" 1.0 0 -16777216 true "Mprice" 1.0 0 -2674135 true MONITOR 107 55 217 100 Market Price Mprice 2 1 11 SLIDER 223 174 383 207 rich-endowment rich-endowment 1000 5000 3000 100 1 NIL HORIZONTAL SLIDER 223 207 383 240 poor-endowment poor-endowment 100 500 300 10 1 NIL HORIZONTAL SLIDER 223 141 384 174 %-of-rich-agents %-of-rich-agents 0 100 50 5 1 NIL HORIZONTAL MONITOR 398 10 579 55 Number of Transactions #-of-transactions 17 1 11 MONITOR 398 55 579 100 Number of Uninformed count uninformed 17 1 11 MONITOR 398 145 579 190 Mean of Endowment of Uninformed totalEU / (count uninformed) 2 1 11 SLIDER 223 109 384 142 %-of-informed %-of-informed 0 100 30 1 1 NIL HORIZONTAL MONITOR 398 100 579 145 Number of Informed count informed 17 1 11 MONITOR 398 190 579 235 Mean of Endowment of Informed totalEI / (count informed) 2 1 11 SWITCH 10 104 180 137 Sales-not-available? Sales-not-available? 1 1 -1000 SLIDER 10 138 180 171 Pr-sales-not-available Pr-sales-not-available 0 100 50 1 1 NIL HORIZONTAL SWITCH 10 172 180 205 Purchases-not-available? Purchases-not-available? 1 1 -1000 SLIDER 10 205 180 238 Pr-purchases-not-available Pr-purchases-not-available 0 100 50 1 1 NIL HORIZONTAL @#$#@#$#@ WHAT IS IT? ----------- The aim of our program is study a financial market in which a single stock is traded with a market price that can be different from free-arbitrage price because of lack of information about fair price, and analyze the convergence between the two prices. There are two types of agents: - informed: which behaviour is consistent with arbitrage pricing theory (they buy the stock when the market price is lower than fair price, viceversa they sell the stock when the market price is higher than free-arbitrage price); - uninformed: which sell or buy the security randomly. This behaviour causes the disalignment of the prices. HOW IT WORKS ------------ Turtles represent the agents: grey turtles are uninformed operators and the red ones are informed. Green patches stand for branches of a unique bank and they are placed randomly. Free arbitrage price dynamic follows a sinusoidal subjects to random shocks. Agents move randomly and when they enter in a bank they do a transaction. Every transaction have two types of consequences: - agent's endowmnet increase if he has bought the stock when the market price was lower than fair price or he has sold the stock when the market price was higher than free-arbitrage price. On the contrary the endowment decreases; - market price moves consistently with the type of transaction: it goes up if the agent has purchased the stock, it goes down if he has sold it. Endowment and market price momevents are directly proportional to the amount of the operation. Market price cannot go up or down more than 90% of the fair price. We consider that market price is egual to free-arbitrage price if its difference is smaller than 1%. Furthermore we have created switches with which asymmetry can be introduced; this means that it will be harder for agents sell or buy the stock. HOW TO USE IT ------------- Initially we have to choice: - the number of operators active on the market; - the percentage of informed agents; - the percentage of rich agents ; - the amount of the endowment of rich people; - the amount of the endowment of poor people; - the number of branches of the banks; Moreover we can introduce asymmetry in purchasing or/and selling the stock, in particular we can: - switch on the inability to find a counterpart in the transaction; - choose the probability with which agents cannot find a counterpart. Clicking the setup button we can create a world with features selected. Clickint the go buttun we start the simulation. If we want to stop the simulation we have to clik the go buttun again. The asymmetry can be introduced also when the simulation is running. The agents go out the market when their endowment is less than 0.1 and the simulation stops when there are no agents. There are some boxes in which we can observe: - the number of operators divided into the two categories; - the mean of the endowment of each categories; - the number of transactions; - market price; - free-arbitrage price. A graph shows prices trend. THINGS TO NOTICE ---------------- If we can buy or sell the stock without limits we can note that the convergence between the two prices depends on: - the number of informated agents: if there are any informated people the market price and the fair price are completely independent; otherwise if we introduce a percentage of informed we start to notice a relationship between the prices. Initially with a small presence of informed (about 5%) there is a convergence but, the volatily of the market price is high. If we want to reduce this volatility we have to increase the number of informed. - the number of banks. If there are limits to the agents operativeness we can note that: - if only purchases are limited, market price tend to be lower than the fair price because if market price goes under the free arbitrage price it is hard for arbitrageurs absorbe, with their operations, the arbitrage opportunity. - if only sells are limited, market price tend to be higher than the fair price because if market price goes upon the free arbitrage price it is hard for arbitrageurs absorbe, with their operations, the arbitrage opportunity. - if neither purchases nor sells are available, it is hard to get a convergence. THINGS TO TRY ------------- If we try to set the slider called "Pr-sales-not-available" to 100%, sales are not permitted, so the informed cannot do any operations while uninformed can only buy, therefore market price can only increase. The same thing happens when we set the slider called "Pr-purchases-not-available" to 100%, but obviously the market price can only decrease. 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