; Marek Spisak & Roman Sperka ; 2011 ; Transaction Costs in Financial Market patches-own [ behavior ; fundamental = 0 / technical trader = 1 indicator ; allows to count traders ] ;------------------------------------------------------------------------------------ globals [ log-price ; current price calculated last-price ; price in time t-1 returns ; log price changes (percentage of current price) F ; fundamental value of the asset orders-by-technical-rules ; orders triggered by technical trading rules orders-by-fundamental-rules ; orders triggered by fundamental trading rules orders-by-technical-rules2 ; orders triggered by technical trading rules in previous run orders-by-fundamental-rules2 ; orders triggered by fundamental trading rules in previous run orders-by-technical-rules3 ; orders triggered by technical trading rules in pre-previous run orders-by-fundamental-rules3 ; orders triggered by fundamental trading rules in pre-previous run weight-technical-traders ; weight of technical traders weight-fundamental-traders ; weight of fundamental traders fitness-technical-rules ; fitness (attractiveness) of technical trading rules fitness-fundamental-rules ; fitness (attractiveness) of fundamental rules fitness-technical-rules2 ; fitness (attractiveness) of technical trading rules in previous run fitness-fundamental-rules2 ; fitness (attractiveness) of fundamental rules in previous run K ; number of technical traders K2 ; number of technical traders in previous run N ; total number of traders alpha ; random term to price calculation beta ; random term to technical-rule decision gamma ; random term to fundamental-rule decision agent2-behavior ; behavior of the randomly selected agent talks-done ; number of already finished agents discussions probab-change-tech-fund ; probability that technical agent will change to fundamental probab-change-fund-tech ; probability that fundamental agent will change to technical transition-prob-tech-plus ; transition probability for technical grow transition-prob-tech-minus ; transition probability for fundamental grow transition-prob ; global transition probability ] ;------------------------------------------------------------------------------------ to setup ;; (for this model to work with NetLogo's new plotting features, ;; __clear-all-and-reset-ticks should be replaced with clear-all at ;; the beginning of your setup procedure and reset-ticks at the end ;; of the procedure.) __clear-all-and-reset-ticks ; = clear-all clear-all-plots ; preparing traders ask patches [ set indicator 1 set behavior (random-float 1) ifelse behavior < 0.5 [ set behavior 0 set pcolor black ] [ set behavior 1 set pcolor yellow ] ] ; setting the default values set log-price 0 set last-price 0 set returns 0 set weight-technical-traders 0 set weight-fundamental-traders 0 set orders-by-technical-rules 0 set orders-by-technical-rules2 0 set orders-by-technical-rules3 0 set orders-by-fundamental-rules 0 set orders-by-fundamental-rules2 0 set orders-by-fundamental-rules3 0 set fitness-technical-rules 0 set fitness-technical-rules2 0 set fitness-fundamental-rules 0 set fitness-fundamental-rules2 0 set F 0 set K2 0 set N sum [indicator] of patches set K sum [indicator] of patches with [behavior = 1] end ;------------------------------------------------------------------------------------ to go if ticks >= 5000 [stop] if ticks > 2 [agent-talk-and-decision] market-clearing tick do-plot end ;------------------------------------------------------------------------------------ ; agents are going to decide to agent-talk-and-decision set talks-done 0 while [talks-total >= talks-done] [ ; selecting first discussing agent (the one that may adopt his opinion) ask patch random-xcor random-ycor [ ;asking the second agent for behavior set agent2-behavior [behavior] of patch random-xcor random-ycor if behavior = 0 and not(agent2-behavior = behavior) [ if (fitness-technical-rules > fitness-fundamental-rules) and (transition-prob > minimal-transaction-prob) [ set pcolor yellow set behavior 1 ] ] if behavior = 1 and not(agent2-behavior = behavior) [ if (fitness-technical-rules < fitness-fundamental-rules) and (transition-prob > minimal-transaction-prob) [ set pcolor black set behavior 0 ] ] ] set talks-done talks-done + 1 ] end ;------------------------------------------------------------------------------------ ; Market clearing mechanism to market-clearing set alpha random-normal 0 sigma-alfa set beta random-normal 0 sigma-beta set gamma random-normal 0 sigma-gamma ; calculating technical rules orders set orders-by-technical-rules3 orders-by-technical-rules2 set orders-by-technical-rules2 orders-by-technical-rules set orders-by-technical-rules (b * (log-price - last-price) + beta) ; calculating fundamental rules orders set orders-by-fundamental-rules3 orders-by-fundamental-rules2 set orders-by-fundamental-rules2 orders-by-fundamental-rules set orders-by-fundamental-rules (c * (F - log-price) + gamma) ; calculating weights set K2 K set K sum [indicator] of patches with [behavior = 1] set weight-technical-traders (K / N) set weight-fundamental-traders ((N - K) / N) ; price updates set last-price log-price set log-price (last-price + a * (orders-by-technical-rules * weight-technical-traders + orders-by-fundamental-rules * weight-fundamental-traders) + alpha) + transaction-costs-amount ifelse last-price = 0 [set returns 0.0] [set returns (log-price - last-price)] ; fitness rules calculation set fitness-technical-rules2 fitness-technical-rules set fitness-fundamental-rules2 fitness-fundamental-rules set fitness-technical-rules (((exp log-price) - (exp last-price)) * orders-by-technical-rules3 + d * fitness-technical-rules2) set fitness-fundamental-rules (((exp log-price) - (exp last-price)) * orders-by-fundamental-rules3 + d * fitness-fundamental-rules2) ; probabilities that agents change their oppinion and use different rules ifelse (fitness-technical-rules > fitness-fundamental-rules) [ set probab-change-fund-tech 0.5 + lambda set probab-change-tech-fund 0.5 - lambda ] [ set probab-change-fund-tech 0.5 - lambda set probab-change-tech-fund 0.5 + lambda ] set transition-prob-tech-plus ((N - K2) / N) * (epsilon + probab-change-fund-tech * (K2 / (N - 1))) set transition-prob-tech-minus (K2 / N) * (epsilon + probab-change-tech-fund * ((N - K2) / (N - 1))) set transition-prob 1 - transition-prob-tech-plus - transition-prob-tech-minus end ;------------------------------------------------------------------------------------ ; Presenting the results in plots to do-plot set-current-plot "log-price" set-current-plot-pen "default" plot log-price set-current-plot "returns" set-current-plot-pen "default" plot returns set-current-plot "weights" set-current-plot-pen "default" plot weight-technical-traders set-current-plot "transition-prob-tech" set-current-plot-pen "transition-prob-tech-plus" plot transition-prob-tech-plus set-current-plot-pen "transition-prob-tech-minus" plot transition-prob-tech-minus set-current-plot-pen "transition-prob" plot transition-prob end ;------------------------------------------------------------------------------------ @#$#@#$#@ GRAPHICS-WINDOW 922 52 1288 439 100 100 1.7711443 1 10 1 1 1 0 1 1 1 -100 100 -100 100 0 0 1 ticks 30.0 BUTTON 9 12 76 45 NIL SETUP NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 87 13 150 46 NIL GO T 1 T OBSERVER NIL NIL NIL NIL 1 SLIDER 14 57 186 90 a a 0 1 1 0.01 1 NIL HORIZONTAL SLIDER 15 97 187 130 b b 0 1 0.05 0.01 1 NIL HORIZONTAL SLIDER 14 136 186 169 c c 0 1 0.02 0.01 1 NIL HORIZONTAL SLIDER 13 216 185 249 epsilon epsilon 0 1 0.1 0.01 1 NIL HORIZONTAL SLIDER 14 176 186 209 d d 0 1 0.95 0.01 1 NIL HORIZONTAL SLIDER 14 256 186 289 lambda lambda 0 1 0.45 0.01 1 NIL HORIZONTAL SLIDER 14 295 186 328 sigma-alfa sigma-alfa 0 1 0.0025 0.0001 1 NIL HORIZONTAL SLIDER 15 332 187 365 sigma-beta sigma-beta 0 1 0.025 0.0001 1 NIL HORIZONTAL SLIDER 15 371 187 404 sigma-gamma sigma-gamma 0 1 0.0025 0.0001 1 NIL HORIZONTAL PLOT 204 53 910 213 log-price time log price 0.0 5000.0 -0.5 0.5 true false "" "" PENS "default" 1.0 0 -16777216 true "" "" PLOT 204 224 911 389 returns time return 0.0 5000.0 -0.06 0.06 true false "" "" PENS "default" 1.0 0 -16777216 true "" "" PLOT 205 405 911 557 weights time weight 0.0 5000.0 0.0 1.0 true false "" "" PENS "default" 1.0 0 -16777216 true "" "" SLIDER 16 412 188 445 talks-total talks-total 1 1000 100 1 1 NIL HORIZONTAL PLOT 208 571 907 721 transition-prob-tech NIL NIL 0.0 5000.0 0.0 1.0 true true "" "" PENS "transition-prob-tech-plus" 1.0 0 -1184463 true "" "" "transition-prob-tech-minus" 1.0 0 -16777216 true "" "" "transition-prob" 1.0 0 -10899396 true "" "" SLIDER 16 453 190 486 minimal-transaction-prob minimal-transaction-prob 0 1 0.51 0.05 1 NIL HORIZONTAL SLIDER 12 493 45 729 transaction-costs-amount transaction-costs-amount 0 0.1 0.0080 0.001 1 NIL VERTICAL @#$#@#$#@ ## Transaction Costs in Financial Market ## WHAT IS IT? Spišák, M. and Šperka, R. (2014): Transaction Costs in Financial Market. Netlogo v. 5.01 simulation. http://ccl.northwestern.edu/netlogo/models/community/Transaction%20Costs%20in%20Financial%20Market.nlogo ## HOW IT WORKS The base model developed by Frank Westerhoff (Westerhoff, 2009) was chosen for the implementation. It is an agent-based model, which simulates the financial market. Two base types of traders are represented by agents: * fundamental traders, whose reactions are based on fundamental analysis - they believe that asset prices in long term approximate their fundamental price - they buy assets when the price is under fundamental value * technical traders, who decide using technical analysis - prices tend to move in trends - by their extrapolating there comes the positive feedback, which can cause the instability Price changes are reflecting current demand excess. This excess is expressing the orders amount submitted by technical and fundamental traders each turn and the rate between their orders evolves in a time. Agents regularly meet and they are discussing their trading performance. One agent can be persuaded by the other to change his trading method, if his rules relative success is less than the others one. Communication is direct talk one agent with other. Talking agents meets randomly - there is no special relationship between them. The success of rules is represented by current and passed myoptic profitability. It is very important to mention, that model assumes traders ability to define the fundamental value of assets and they are behave rationally. The price is reflecting the relation between assets that have been bought and sold in a turn and the price change caused by these orders. This can be formalized as a simple log-linear price impact function. P_(t+1)= P_t+a(W_t^C D_t^C+ W_t^F D_t^F )+ ?_t Where a is positive price adjustment coefficient, D^C are orders generated by technical angents while D^Fare orders of fundamental ones. W^C and W^Fare weights of the agents using technical respective fundamental rules. They are reflecting current ratio between the technical and fudamental agents. ? brings the random term to Figure 1. It is an IID normal random variable with mean zero and constant standard deviation ?^?. As was already said, technical analysis extrapolates price trends - when they go up (price is growing) agents buy the assets. So the formalization for technical order rules can be like this D_t^C=b(P_t- P_(t-1) )+ ?_t The parameter b is positive and presents agent sensitivity to price changes. The difference in brackets reflects the trend and ? is the random term - IID normal random variable with mean zero and constant standard deviation ?^?. Fundamental analysis permits the difference between price and fundamental value for short time only. In long run there is an aproximation of them. So if the price is below the fundamental value - the assets are bought and vice versa - orders according fundamentalists are formalized D_t^F=c(F- P_t )+ ?_t c is positive and presents agent sensitivity to reaction. F represents fundamental value - we keep as constant value to keep the implementation as simple as possible . ? is the random term - IID normal random variable with mean zero and constant standard deviation ?^?. If we say that N is the total number of agents and K is the number of technical traders, then we define the weight of technical traders W_t^C= K_t/N and the weight of fundamental traders W_t^F=(N- K_t)/N Two traders meet at each step and they are discussing about the success of their rules. If the second agent rules are more successful, the first one changes its behavior with a probability K. Probability of transition is defined as (1-?). Also there is a small probability ? that agent changes his mind independently. Transition probability is formalized as K_(t-1)(t) {?(K_(t-1)+1 with probability p_(t-1)^+= (N- K_(t-1))/N (?+(1-?)_(t-1)^(F?C) K_(t-1)/(N-1))@K_(t-1)-1 with probability p_(t-1)^-= ( K_(t-1))/N (?+(1-?)_(t-1)^(C?F) (N- K_(t-1))/(N-1))@K_(t-1) with probability 1+? p?_(t-1)^+- p_(t-1)^- )? where the probability that fundamental agent becomes technical one is (1-?)_(t-1)^(F?C)={?(0.5+? for A_t^C>A_t^F @0.5-? otherwise )? respective that technical agent becomes fundamental one is (1-?)_(t-1)^(C?F)={?(0.5-? for A_t^C>A_t^F @0.5+? otherwise )? Success (fitness of the rule) is represented by past myoptic profitability of the rules that are formalized as A_t^C=(exp?[P_t ]-exp?[P_(t-1) ] ) D_(t-2)^C+dA_(t-1)^C for the technical rules and A_t^F=(exp?[P_t ]-exp?[P_(t-1) ] ) D_(t-2)^F+dA_(t-1)^F for the fundamental rules. Agents use most recent performance (at the end of A_^C formula resp. A_^F) and also the orders submitted in period t-2 are executed at prices started in period t-1. In this way the myoptic profits are calculated. Agents have memory - which is represented by parameter d. Values are 0 ? d ? 1. If d = 0 then agent has no memory, much higher value is, much higher influence the myoptic profits have on the rule fitness. ## EXTENDING THE MODEL WITH TRANSACTION COSTS The aim of the model is to investigate the influence of the transaction costs on the market stability (which is measured by the price volatility - much more stable the market is, much less are price differences in a time). The entrance of transaction costs (TC) - e.g. as a tax will have direct impact on the asset price. The model was little changed to adopt also this aspect into price. So price is composed this way: P_(t+1)= P_t+a(W_t^C D_t^C+ W_t^F D_t^F )+ ?_t+TC Where TC is a value of the transaction costs, which is constant during all the simulation. While the tax is out-of trade factor, all the agents will be affected in the same way. Generally there can be also different transaction costs than taxes - e.g. information obtaining costs. The TC increase has following results: * price increase will stimulate technical rules usage, it-s influence on expected future profit opportunities (as the fundamental value of asset) is irrelevant - they depend on the company state, rather than on transaction costs * in a short time, the price grow will attract technical traders, but after the realized profits will fall down and the fundamental traders will start to dominate, it will lead to market stabilization (price changes are falling - volatility of price is lower) ## HOW TO USE IT In the interface section set the values for the parameters, SETUP and RUN the model. ## THINGS TO NOTICE The most important thing to notice is price and technical traders percent envolvement based on the enterd transaction costs amount. ## THINGS TO TRY Try to set high and low tranaction costs to see the influence on the price and technical traders percent. ## CREDITS AND REFERENCES This model was developed with the support by grant of Silesian University no. SGS/6/2013 "Advanced Modeling and Simulation of Economic Systems”. This model was described and analysed in detail in these papers: ŠPERKA, R., SPIŠÁK, M. Transaction Costs Influence on the Stability of Financial Market: Agent-based Simulation. Journal of Business Economics and Management, Taylor & Francis, London, United Kingdom, 2013. Volume 14, Supplement 1, pp. S1-S12, DOI: 10.3846/16111699.2012.701227. Print ISSN 1611-1699, Online ISSN 2029-4433. Available from: . ŠPERKA, R., SPIŠÁK, M. Tobin Tax Introduction and Risk Analysis in the Java Simulation. In: Proc. 30th International Conference Mathematical Methods in Economics. Part II. Silesian University in Opava, Karvina, Czech Republic, 11.-13.9.2012, pp. 885-890, ISBN 978-80-7248-779-0. Available from: < http://mme2012.opf.slu.cz/proceedings/pdf/152_Sperka.pdf>. SPIŠÁK, M., ŠPERKA, R. Financial Market Simulation Based on Intelligent Agents - Case Study. Journal of Applied Economic Sciences, Volume VI, Issue 3(17), Fall 2011, Spiru Haret University: Romania, ISSN 1843-6110, pp. 249-256. 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