Vol. 47 No. SIG 14(TOM 15) Oct. 2006 RBF 2 Effect of Stock Investor Agent According to Framing Effect to Stock Exchange in Artificial Stock Market Zhai Fei, Shen Kan, Yusuke Namikawa and Eisuke Kita Several psychological biases should be taken into consideration in the actual stock exchange. In this paper, we discuss the effect of the framing effect to it. The stock investor agent is defined by using the RBF neural network. The prediction of the agent shows that the agent behaviour follows the framing effect. The stock exchange by the agents is performed in the artificial market. The characteristics of the stock price fluctuations in the actual and artificial markets are compared in order to discuss the effect to the agents accodring to the framing effect. Artificial markets are comstructed with the agents of which prediction rules are learned by short and long moving average data. In the market of many agents learned with long-run moving average data, the features of the stock price fluctuation are similar to them of the actual market. 1. 1) 20 1 Graduate School of Information Sciences, Nagoya University NTT NTT Data Co. 2) 129
130 Oct. 2006 Radial Basis Function RBF 2. 2.1 Efficient Market Hypothesis Fama 1970 3) 4) 1 Fig. 1 Utility function. 2 Fig. 2 Value function. (1) (2) (3) (4) (5) 1 2.2 Behavioral Finance
Vol. 47 No. SIG 14(TOM 15) 131 5),6) 1 2 7) reference point 8) 8) 10) 2.3 7) (1) anchoring adjustment (2) hindsight bias (3) representativeness heuristics (4) availability bias (5) framing effect 2.4 11) 2),10) 3. 3.1 3 (1) 3 Fig. 3 Artificial market model.
132 Oct. 2006 (2) 4 RBF Fig. 4 RBF neural network. (3) 3.2 RBF RBF 3.2.1 RBF RBF 4 1 F (x) Φ i (x) (1) 12),13) n F (x) = ω i Φ i (x) (1) i=1 Φ i (x) (2) ( Φ i (x) =exp (x c ) i) 2 (2) σi 2 Φ i (x) c i σ i i ω i 14) 3.2.2 RBF 3 c i σ i ω i RBF c i σ i 2 RBF c i k-means k ω i 3.2.2.1 k-means k-means N x i i =1 n k G i i =1 k 12),13) k-means Step1 k c i Step2 c i (3) (4) x i G i ( T ) 1 2 D(x, c) = (x k c k ) 2 (3) k=1 D(x i,c j ) <D(x i,c l ) j l (4) Step3 (5) c i c i = 1 x j (5) G i x j G i G i G i Step4 c j Step2 3.2.2.2 k k
Vol. 47 No. SIG 14(TOM 15) 133 Moving Average MA J.E. 15) t P t n 5 Fig. 5 Back propagation. σ i 12),13) i σ i c i k σ i = 1 k c i c j (6) k j=1 c j j =1...k c i k k 3.2.3 5 ω i E E (7) y i o i (w i ) E ω i (ω i ) old (ω i ) old ω i (ω i ) old ω i (8) (ω i ) new 13) E = 1 n (y i o i (w i )) 2 (7) 2 i (ω i ) new =(ω i ) old + ω i (8) (ω i ) old E ω i η ω i (9) ω i = η E ω i (9) η η 3.3 RBF MA P t y i MA = P 0 + P 1 + + P n 1 (10) n 3.4 2 1,000,000 10,000 P t (1) P t >P t 1 O t / O t =(M t Pt ) P t P t 1 α (11) P t 1 (2) P t <P t 1 O t O t = S t P t 1 P t P t 1 α (12) P t P t t t M t t S t t α 3.5 S t = S t + Ot (13) M t = M t P t Ot (14)
134 Oct. 2006 S t = S t Ot (15) M t = M t + P t Ot (16) P t O t M t S t M t t t t t S t t O t Ot Ot RBF 3.6 3.6.1 16) 3.6.2 16),17) 3.7 RBF t t max t rel t rel t rel =30 (1) (2) RBF (3) t t 0 (4) RBF (5) (6) (7) (8) (9) t t +1 (10) Mod(t, t rel )=0(4) Mod(t, t rel ) t t rel (11) t<t max (5) 4. 4.1 3 RBF
Vol. 47 No. SIG 14(TOM 15) 135 6 Fig. 6 Stock price with increasing trend. 5 30 5 30 2 5000 η =0.6 RBF 10 20 1 200 100 5 1 30 2 4.1.1 6 5 30 6 200 5 30 7 8 201 Real price Agent1 Agent2 5 30 7 8 1 Fig. 7 Prediction of Agent 1 for stock price with increasing trend. 2 Fig. 8 Prediction of Agent 2 for stock price with increasing trend. Fig. 9 9 Stock price with decreasing trend. 5 1 30 2 4.1.2 9 5 30
136 Oct. 2006 10 1 Fig. 10 Prediction of Agent 1 for stock price with decreasing trend. 11 2 Fig. 11 Prediction of Agent 2 for stock price with decreasing trend. 5 30 10 11 5 1 30 2 4.2 6 200 5 30 2 100 5 30 2 2 10,000 1,000,000 100 30 n n =1, 2, 3... 1 5 2 30 2 5 1 1 2 1 75% 2 25% 3 1 2 50% 4 1 25% 2 75% 5 2 4.2.1 5 1 2 12 13 14 15 16 1 2 1 5 1 2 1 1 1 5 1 3 1
Vol. 47 No. SIG 14(TOM 15) 137 12 1 Fig. 12 Accuracy of predicted stock price in Market 1. 16 5 Fig. 16 Accuracy of predicted stock price in Market 5. Table 1 1 Average value of accuray of predicted stock price. Market Agent 1 Agent 2 1 0.069 2 0.217 0.078 3 0.190 0.141 4 0.190 0.077 5 0.065 13 2 Fig. 13 Accuracy of predicted stock price in Market 2. 17 1 Fig. 17 Volume of dealing in Market 1. 14 3 Fig. 14 Accuracy of predicted stock price in Market 3. 15 4 Fig. 15 Accuracy of predicted stock price in Market 4. 1 4.2.2 5 17 18 2 Fig. 18 Volume of dealing in Market 2. 18 19 20 21 2
138 Oct. 2006 19 3 Fig. 19 Volume of dealing in Market 3. 22 1 Fig. 22 Stock price and its volatility in Market 1. 20 4 Fig. 20 Volume of dealing in Market 4. 23 2 Fig. 23 Stock price and its volatility in Market 2. 21 5 Fig. 21 Volume of dealing in Market 5. 1 50 60 4.2.3 5 22 23 24 25 26 = 100 (%) (17) 1 24 3 Fig. 24 Stock price and its volatility in Market 3. 5 1 5 1 1 1 2 1 1
Vol. 47 No. SIG 14(TOM 15) 139 25 4 Fig. 25 Stock price and its volatility in Market 4. 27 1 Fig. 27 Frequency distribution of volatility in Market 1. 28 2 Fig. 28 Frequency distribution of volatility in Market 2. 26 5 Fig. 26 Stock price and its volatility in Market 5. 2 1 5 1 1 4.3 15),18),19) 27 28 29 30 31 1 5 IBM 2003 10 2004 2 100 29 3 Fig. 29 Frequency distribution of volatility in Market 3. 30 4 Fig. 30 Frequency distribution of volatility in Market 4. 32 1 5 32 30 31 4 5 5 30 25 : 75 0 : 100 4 5 Self-corelative coefficient of Stock Price: SSP
140 Oct. 2006 3σ PRo3S 4 5 3 30 31 5 Fig. 31 Frequency distribution of volatility in Market 5. 32 IBM 2003 10 2004 2 Fig. 32 Frequency distribution of IBM Stock price volatility (2003 Oct. 2004 Feb.). 2 Table 2 Parameter of return. Parameter Real Market SSP 0.05 0.10 SSC 0.40 0.60 PRi1S 0.75 0.80 PRo3S 0.01 0.02 3 Table 3 Parameter estimated at artificial markets. Market Parameter 1 2 3 4 5 SSP 0.60 0.47 0.35 0.21 0.02 SSC 0.09 0.41 0.43 0.92 0.91 PRi1S 0.42 0.67 0.78 0.75 0.74 PRo3S 0.017 0.00 0.01 0.00 0.00 Self-correlation coefficient of Stoch Change rate: SSC 1σ Probability of Return in 1 Sigma: PRi1S 3σ Probability of Return out of 3 Sigma: PRo3S 2 20) 5 3 SSP SSC 1σ PRi1S 3 4 5 5. Radial Basis Function RBF 2 2 21 COE
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