Springer artificial economics agent based methods in finance game theory and their applicationsspringer(2006)

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/HFWXUH1RWHVLQ(FRQRPLFV DQG0DWKHPDWLFDO6\VWHPV   )RXQGLQJ(GLWRUV 0%HFNPDQQ +3.Q]L 0DQDJLQJ(GLWRUV 3URI'U*)DQGHO )DFKEHUHLFK:LUWVFKDIWVZLVVHQVFKDIWHQ )HUQXQLYHUVLWlW+DJHQ )HLWKVWU$9=,,+DJHQ*HUPDQ\ 3URI'U:7URFNHO ,QVWLWXWIU0DWKHPDWLVFKH:LUWVFKDIWVIRUVFKXQJ ,0: 8QLYHUVLWlW%LHOHIHOG 8QLYHUVLWlWVVWU%LHOHIHOG*HUPDQ\ (GLWRULDO%RDUG $%DVLOH$'UH[O+'DZLG.,QGHUIXUWK:.UVWHQ86FKLWWNR  3KLOLSSH0DWKLHX %UXQR%HDXILOV 2OLYLHU%UDQGRX\ (GV $UWLILFLDO(FRQRPLFV   $JHQW%DVHG0HWKRGVLQ)LQDQFH *DPH7KHRU\DQG7KHLU$SSOLFDWLRQV   (GLWRUV 3URI3KLOLSSH0DWKLHX /,)/867/&LWp6FLHQWLILTXH 9LOOHQHXYHG·$VFT&HGH[ SKLOLSSHPDWKLHX#OLIOIU 3URI2OLYLHU%UDQGRX\ &/$5((867/ $YHQXHGX3HXSOH%HOJH /LOOH&HGH[)UDQFH ROLYLHUEUDQGRX\#XQLYOLOOHIU 'U%UXQR%HDXILOV /,)/867/&LWp6FLHQWLILTXH 9LOOHQHXYHG·$VFT&HGH[ EUXQREHDXILOV#OLIOIU /LEUDU\RI&RQJUHVV&RQWURO1XPEHU ,661 ,6%16SULQJHU%HUOLQ+HLGHOEHUJ1HZ 0.7 means selling S-MA and F-MA determine the limit price by the moving average (MA) of spot and futures price respectively MA is an average of the latest n terms' prices and its value is given by MA(n) = (l/n)i:;j=ipn SF-SPR determines a kind of order by the spread index SPR SPR is obtained by SPR = (pf — PS)IPS' PS is the latest spot price, and pf is the latest futures prices When SPR > E, SF-SPR makes a selling order, and when SPR < —E makes a buying order, where -E is a threshold value for making order DAY-BS makes a selling order, with the latest future prices plus a fixed amount, and makes a buying order with the latest futures price plus a fixed amount As for these technical analyses, see Murphy [6, 7], and Tanaka [9] 230 Shingo Yamamoto et al 2.2 Independent Variables In the previous studies of artificial market, it is much common to investigate the effect of modifying the TA's trade strategies and/or the proportions of TAs in a market, or the effect of changing the market institutions, on RI, CR, and volatility (Deguchi et al [2], Fukushima [3], Nakajima et al [8]) However, to the best of our knowledge, there are few studies concerning with the order determination algorithm So we investigated the effects of changing order quantity determination algorithms on RI and CR in this research First, for the decision-maker (DM), we consider the following two cases; (1) TA itself is a DM, (2) a meta TA is a DM When TA itself is a DM, the TA determines order quantity according to a given probability distribution When a meta TA is a DM, the meta TA allots a constant order quantity to each TA according to a given probability distribution For the order quantity distribution (OD), we compare exponential distribution^, which is observed in real-world market, uniform distribution^,which is provided by U-Mart standard AS, normal distribution^, and a constant For the size of order quantity, according to Fukushima [3], we used following four sets of average m and variance cr^, (m, a^) = (10, 20), (20, 90), (30, 210), (50, 600)^ For the price information (PI), we used J30 price information, from 29 December, 1989 to 29 November, 1999, which is given by U-Mart system In our experiment, we divided this Pis into following four patterns of time series; "Up", "Down", "Bound", and "Oscillation" as in U-Mart International Experiment (UMIE) tournament determined by UMIE2004 System Operational Committee [10] Time series of these spot prices are shown in Fig Thus, our experimental condition can be expressed by four-factors (DM, OD, m, PI) Table summarizes these experimental conditions.^^ ^ Probability density function is f{x) = Xe~^^, average is 1/A, and variance is 1/A^ ^ Probability density function is f{x) = 1/(6 — a) (if a < x < b ) , f{x) = (otherwise), average is 1/(6 — a), and variance is (6 — a)^/12 Probability density function is f{x) = J - e 2^^, average is fi, and variance is a ^ If OD = const., a^ = If OD is uniform distribution, for letting (m, cr^) same as those in other distributions as possible, we set {m,a^) as follows; (m,cr^)=(10, 19), (20, 91), (30, 217), (50, 602) ^° In other word, our experiment can be seen the following multiple linear regression model with dummy variables to investigate the effect of four factors on RI and CR (For the detail of multiple liner regression model, see Greene [4]) First, D"^, Dt, Dt DI, D^, D ? , D J , D^, D^, D^ are dummy variables If D"^ = 1, TA itself is a DM, IfD"^ = 0, meta TA is a DM If D? = 1, OD is exponential distribution IfDi = 1, OD is uniform distribution If D^ = 1, OD is normal distribution If Df = 0{i = 1,2, 3), OD is constant lfDi = hm= 10 lfD^ = l,m = 20 IfD^, m = 30 If Dt = 0{i = l,2,3), m = 50 Then, If D^ = 1, PI is UP If D^ = 1, PI is Down, If Dg = 1, PI is Bound If Df = 0{i = 1, 2,3), PI is Oscillation How Order Distributions Affect the RI and CR 3800 PI = Up Pl = Down Đ3800 >^ 2800 Q - 231 1 h (^1800 = 3800 120 120 240 PI = Bound §3800 120 120 240 PI = Oscillation 2800 o Q CO 1800 120 120 240 240 Fig Time series of the spot prices Table Four factors in our experiment Factor DM OD IfiTA itself Ifi Expotential 3fi Normal m((7^) Ifi 10 (20) 3fi30(210) Time series of Ifi Up spot price (PI) 3fi Bound 2fimetaTA 2fi Uniform 4fi Constant 2fi20(90) 4fi50(600) 2fiDown 4fi Oscillation It seems that we should run x x x = 128 different experiments as shown in Table However, when the OD = (Constant), each TA's order quantity is the same regardless of who is a DM So, it is enough to run 112 experiments We run computer simulations 50 times for each of 112 experimental conditions as in UMIE (UMIE2004 System Operational Committee [10]) 2.3 Dependent Variables In our experiment, by manipulating experimental conditions explained in the previous subsection, we analyzed how changing order quantity distribution affects RI and CR So, RI and CR are dependent variables in our experiment RI is defined as RI = {LOT — ^o)/^o where UJQ is the initial amount of fund and LOT is the amount of money at the final round T CR is defined as CR — Nc/Nt, Thus, y = a-\- PV^ + Yfi^ihiDf + 6iD? + SiDf) is our regression model, where y =RI or y =CR, and at, j3i,ji,6i, and Si (i = 1,2,3)) are coefficients to be estimated 232 Shingo Yamamoto et al where Nt is the number of orders made at the day t and A^c is the number of order quantity that is contracted at the day t Results 3.1 The Distribution of Order Quantity Figure shows the distributions of order quantity in the market as a whole when DM =TA, OD = Exp., m = 20, PI = all ^^ 11 21 31 41 51 61 71 Fig OD in the market as a whole when each TA's OD is Exponential At a glance, in the cases of exponential distribution, the distributions of order quantity in the market as a whole corresponded to each TAs' order distributions For the other distributions, same results are hold 3.2 The Analysis of Rl and CR We show the maximum value of average CR for each (DM, OD, PI) in Table Average CR attains the maximum in all cases when m = 10 When ODs were Constant and m = 30, average value of CR also attains the maximum value We also show the maximum value of average CR for each (DM, m, PI) in Table From this table, average CR likely attains the maximum when ODs were Constant (13 out of 32 cases) Further, we show in Table 5, which shows the maximum value of average CR for each combination of (DM, OD, m), for over half of the cases average CR attains maximum when Pis were Down (18 out of 32 cases) The shape of a graph is almost same when m takes other values How Order Distributions Affect the RI and CR Table The maximum value of average CR DM OD PI meta Exp Up meta Exp Down meta Exp Bound meta Exp Osc meta Uni Up meta Uni Down meta Uni Bound meta Uni Osc meta Norm Up meta Norm Down meta Norm Bound meta Norm Osc meta Cons Up meta Cons Down meta Cons Bound meta Cons Osc m 10 10 10 10 10 10 10 10 10 10 10 10 30&10 30&10 30&10 30&10 ]Max value 1DM 0.4139 0.4130 0.4045 0.4119 0.4051 0.4109 0.4131 0.4030 0.3992 0.3973 0.4086 0.4228 0.4111 0.4025 0.4006 0.4014 OD PI TA Exp Up TA Exp Down TA Exp Bound TA Exp Osc TA Uni Up TA Uni Down TA Uni Bound TA Uni Osc TA Norm Up TA Norm Down TA Norm Bound TA Norm Osc TA Cons Up TA Cons Down TA Cons Bound TA Cons Osc m Max value 10 0.4075 10 0.4130 10 0.4110 10 0.4082 10 0.4097 10 0.4135 10 0.4090 10 0.4111 10 0.4084 10 0.4085 10 0.4075 10 0.4112 30&10 0.4111 30&10 0.4025 30&10 0.4006 30&10 0.4014 Table The maximum value of average CR DM m PI meta 10 Down meta 20 Down meta 30 Down meta 50 Down meta 10 Up meta 20 Up meta 30 Up meta 50 Up meta 10 Osc meta 20 Osc meta 30 Osc meta 50 Osc meta 10 Bound meta 20 Bound meta 30 Bound meta 50 Bound OD metax value | DM m PI OD metax value Exp 0.4130 TA 10 Down Uni 0.4135 Exp TA 20 Down Exp 0.4053 0.4050 Cons 0.4025 TA 30 Down Cons 0.4123 Exp 0.3908 TA 50 Down Cons 0.3981 Exp 0.4139 TA 10 Up Cons 0.4114 Exp 0.4046 TA 20 Up Uni 0.4016 Cons 0.4011 TA 30 Up Cons 0.4114 Norm 0.3920 0.3967 TA 50 Up Cons Norm 0.4228 TA 10 Osc Norm 0.4112 Norm 0.4104 TA 20 Osc Norm 0.4047 Cons 0.4014 TA 30 Osc Cons 0.4107 Exp 0.3896 0.3964 TA 50 Osc Cons Uni 0.4131 TA 10 Bound Exp 0.4110 Uni 0.4044 TA 20 Bound Exp 0.3991 Cons 0.4006 TA 30 Bound Cons 0.4102 Uni 0.3890 TA 50 Bound Cons 0.3954 233 234 Shingo Yamamoto et al Table The maximum value of average CR DM OD m PI ]Vlax value 1DM OD m PI Max value meta Exp 10 Up 0.4139 TA Exp 10 Down 0.4130 meta Exp 20 Down 0.4053 TA Exp 20 Down 0.4050 meta Exp 30 Down 0.3999 TA Exp 30 Down 0.3979 meta Exp 50 Down 0.3908 TA Exp 50 Down 0.3872 meta Uni 10 Bound 0.4131 TA Uni 10 Down 0.4135 meta Uni 20 Bound 0.4044 TA Uni 20 Down 0.4030 0.3977 TA Uni 30 Up 0.3930 meta Uni 30 Osc 0.3876 meta Uni 50 Bound 0.3890 TA Uni 50 Up meta Norm 10 Osc 0.4228 TA Norm 10 Osc 0.4112 0.4104 TA Norm 20 Osc 0.4047 meta Norm 20 Osc meta Norm 30 Up 0.3969 TA Norm 30 Osc 0.3972 meta Norm 50 Up 0.3920 TA Norm 50 Down 0.3827 meta Cons 10 Down 0.4025 TA Cons 10 Down 0.4123 meta Cons 20 Down 0.3884 TA Cons 20 Down 0.3981 meta Cons 30 Down 0.4025 TA Cons 30 Down 0.4123 meta Cons 50 Down 0.3884 JjA Cons 50 Down 0.3981 Table The maximum value of average RI DM OD meta Exp meta Exp meta Exp meta Exp meta Uni meta Uni meta Uni meta Uni meta Norm meta Norm meta Norm meta Norm meta Cons meta Cons meta Cons meta Cons PI Up Down Bound Osc Up Down Bound Osc Up Down Bound Osc Up Down Bound Osc m Max value 1DM OD PI 50 0.9917 TA Exp Up 50 0.9910 TA Exp Down 50 0.9908 TA Exp Bound 10 0.9899 TA Exp Osc 50 0.9916 TA Uni Up 50 0.9909 TA Uni Down 50 0.9907 TA Uni Bound 10 0.9899 TA Uni Osc 50 0.9918 TA Norm Up 50 0.9911 TA Norm Down 50 0.9909 TA Norm Bound 10 0.9899 TA Norm Osc 50 0.9919 TA Cons Up 50 0.9911 TA Cons Down 50 0.9910 TA Cons Bound 10 0.9899 TA Cons Osc m Max value 50 0.9919 50 0.9910 50 0.9910 10 0.9899 50 0.9919 50 0.9911 50 0.9911 10 0.9899 50 0.9918 50 0.9910 50 0.9910 10 0.9899 50 0.9919 50 0.9911 50 0.9910 10 0.9899 How Order Distributions Affect the RI and CR Table The maximum value of average RI DM m PI meta 10 Up meta 10 Dov^m meta 10 Bound meta 10 Osc meta 20 Up meta 20 Dowm meta 20 Bound meta 20 Osc meta 30 Up meta 30 Dowm meta 30 Bound meta 30 Osc meta 50 Up meta 50 Dowm meta 50 Bound meta 50 Osc OD ]Max value 1DM m PI OD Max value Exp 0.9906 TA 10 Up Uni 0.9906 Cons 0.9903 TA 10 Dowm Exp 0.9903 TA 10 Bound Cons 0.9899 Exp 0.9900 Uni 0.9899 TA 10 Osc Uni 0.9899 Cons 0.9913 TA 20 Up Cons 0.9913 TA 20 Dowm Exp 0.9907 Cons 0.9906 Exp 0.9901 TA 20 Bound Uni 0.9901 Exp 0.9899 TA 20 Osc Exp 0.9899 TA 30 Up Cons 0.9917 Cons 0.9917 Cons 0.9908 TA 30 Dowm Uni 0.9909 Uni 0.9905 TA 30 Bound Norm 0.9904 TA 30 Osc Uni Exp 0.9898 0.9899 TA 50 Up Cons 0.9919 Cons 0.9919 Cons 0.9911 TA 50 Dowm Cons 0.9911 Cons 0.9908 TA 50 Bound Uni 0.9911 Uni 0.9898 TA 50 Osc Uni 0.9898 Table The maximum average of RI DM OD m PI Max value 1DM OD m PI Max value meta Exp 10 Up 0.9906 TA Exp 10 Up 0.9905 meta Exp 20 Up 0.9911 TA Exp 20 Up 0.9912 meta Exp 30 Up 0.9913 TA Exp 30 Up 0.9915 meta Exp 50 Up 0.9917 TA Exp 50 Up 0.9919 meta Uni 10 Up 0.9906 TA Uni 10 Up 0.9906 meta Uni 20 Up 0.9911 TA Uni 20 Up 0.9912 meta Uni 30 Up 0.9914 TA Uni 30 Up 0.9916 meta Uni 50 Up 0.9916 TA Uni 50 Up 0.9919 meta Norm 10 Up 0.9906 TA Norm 10 Up 0.9905 meta Norm 20 Up 0.9912 TA Norm 20 Up 0.9912 meta Norm 30 Up 0.9915 TA Norm 30 Up 0.9915 meta Norm 50 Up 0.9918 TA Norm 50 Up 0.9918 meta Cons 10 Up 0.9905 TA Cons 10 Up 0.9905 meta Cons 20 Up 0.9913 TA Cons 20 Up 0.9913 meta Cons 30 Up 0.9917 TA Cons 30 Up 0.9917 meta Cons 50 Up 0.9919 TA Cons 50Up 0.9919 235 236 Shingo Yamamoto et al In Table 6, we show the maximum value of average RI for each combination of (DM, OD, PI) The average RI attains maximum in most of the cases when m = 50 (24 out of 32 cases) On the other hand, when Pis were Oscillation, RIs attains maximum when m = 10 From Table 7, where the maximum values of average RI for each combination of (DM, m, PI) are shown Uniform and Constant outperformed in most of cases (10 out of 32 are Uniform, and 12 out of 32 are Constant) Finally, we summarize the maximum value of average RI for each combination of (DM, OD, m) in Table We found that the average RI attained maximum when Pis were Up Conclusions As Kawagoe and Wada [5] point out, there are few studies about strategy determining orders quantity in an artificial market In this research, although strategies we used were so limited, we investigated how differences of order quantity strategy affected RI and CR In our results, we showed that the order distribution in the market as a whole always followed the distribution of each TA's order distribution CR attains the maximum in all cases average when m = 10, and when ODs were Constant, and where Pis were Down The average RI attains maximum in most of the cases when m = 50 Uniform and Constant cases in most of cases The average RI also attained and where ODs were maximum when Pis were Up For designing a successfiil TA, making a TA which can avoid bankruptcy is most difficult Martingale may be a well-known order quantity strategy (Tanaka [9]) However, Martingale is not practical strategy because it lead us to the bankruptcy unless we had large enough money In the previous studies in U-Mart system, two typical cases of bankruptcy were reported as follows; (1) Because of the lack of money at the end of a day, TA could not clear the payment for buying and selling orders, and (2) TA did not anticipate the large cost when it carried over positive or negative positions at the final days Though current standard AS set provided by U-Mart system can avoid bankruptcy of type (1), it doesn't have any position management function So, there is no guarantee to avoid bankruptcy of type (2) Thus, in the future research, it would be worthwhile to incorporate more sophisticated agent into our consideration, who makes orders when current expected benefit derived from those orders is greater than the present discounted value of loss caused by the change in position for that agent References Izumi K (2003) Artificial Market, Morikita publishing (in Japanese) Deguchi H, Izumi K, Shiozawa K, Takayasu Y, Terano H, Sato T, Kita H (1997) "Discussion Socially and scholarly meanings for studying artificial market" The Book of Artificial Interigence Society, 12(1), p 1-8 (in Japanese) Fukushima Y(2001) "The way of order matchings and price change in the JGB fixtures market." The Agency of Money Market, Working Paper Series, 2001-J-1 (in Japanese) How Order Distributions Affect the RI and CR 237 Greene WH (2002) Econometric Analysis, Prentice Hall Kawagoe T, Wada S (2005) "A New Approach to Controlling Artificial Market Conditions", mimeo Murphy JJ (1986) Technical Analysis of the Future Markets, New York Insutitute of Finance Murphy JJ (1997) Study Guide for Technical Analysis of the Future Markets, New York Insutitute of Finance Nakajima Y, Ono I, Sato H, Mori N, Kita H, Matsui H, Taniguchi K, Deguchi H, Terano T, Shiozawa Y (2004) "Introducing Virtual Futures Market System "U-Mart"," Experiments in Economic Sciences - New Approaches to Solving Real-world Problems Tanaka K(1998) A Big Book of Technical Analysis, Sigma Base Capital (in Japanese) 10 UMIE2004 System Operational Committee (2004) "Overview of UMIE2004 — December 1th, 2003 Version" (Appendix of U-Mart developer kit) ... actors against their intentions and welfare although emerging from their choices and being stable and self-maintaining Hayek's theory of spontaneous social order andElster's opposition between intentional... others Following these initial attempts to mix computational approaches and social sciences, for instance among the pioneering works using Agent- based Computational Economics in finance, one can... we introduce forecasting rules Each agent estimates the expected return of investing in the stock under risk and makes his buy/sell order to a predefined price The remaining money is invested in
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