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1.6 1

0.8

1.4

0.6

1.2 0.4

0.2

1

Price

Dex

0

0.8

âˆ’0.2

âˆ’0.4

0.6

âˆ’0.6

0.4

âˆ’0.8

Price

Time

Dex

âˆ’1

0.2

0 5 10 15 20 25 30 35 40 45 50 55 60

Figure 12.2 Dynamics of excess demand (Dex) and price for the model

(12.4.5)â€“(12.4.7) with a Â¼ 1.05, b Â¼ g Â¼ 1, nÃ¾(0) Â¼ 0.4 and p(0) Â¼ 1.05.

can be dropped. The system has three variables (nÃ¾ , nÃ€ , p) and

therefore may potentially describe deterministic chaos (see Chapter

7). Also, one can randomize the model by adding noise to the utility

function (12.4.4) or to the price formation equation (12.4.6). Interest-

ingly, the latter option may lead to a negative correlation between

price and excess demand, which is not possible for the deterministic

equation (12.4.6) [17].

12.4.3 WHY TECHNICAL TRADING SUCCESSFUL

MAY BE

A simple extension of the basic model (12.4.1)â€“(12.4.7) provides

some explanation as to why technical trading may sometimes be

successful [18]. Consider a system with a constant number of traders

N that consists of â€˜â€˜regularâ€™â€™ traders NR and â€˜â€˜technicalâ€™â€™ traders

NT : NT Ã¾ NR Â¼ N Â¼ const. The â€˜â€˜regularâ€™â€™ traders are divided into

buyers, NÃ¾ (t), and sellers, NÃ€ (t): NÃ¾ Ã¾ NÃ€ Â¼ NR Â¼ const. The rela-

tive numbers of â€˜â€˜regularâ€™â€™ traders, nÃ¾ (t) Â¼ NÃ¾ (t)=N and

nÃ€ (t) Â¼ NÃ€ (t)=N, are described with the equations (12.4.2)â€“(12.4.4).

The price formation in equation (12.4.6) is also retained. However,

140 Agent-Based Modeling of Financial Markets

the excess demand, in contrast to (12.4.7), incorporates the â€˜â€˜tech-

nicalâ€™â€™ traders

Dex Â¼ d(nÃ¾ Ã€ nÃ€ Ã¾ FnT ) (12:4:9)

In (12.4.9), nT Â¼ NT =N and function F is defined by the technical

trader strategy. We have chosen a simple technical rule â€˜â€˜buying on

dips â€“ selling on tops,â€™â€™ that is, buying at the moment when the price

starts rising, and selling at the moment when price starts falling

8

< 1, p(k) > p(k Ã€ 1) and p(k Ã€ 1) < p(k Ã€ 2)

F(k) Â¼ Ã€1, p(k) < p(k Ã€ 1) and p(k Ã€ 1) > p(k Ã€ 2) (12:4:10)

:

0, otherwise

Figure 12.3 shows that inclusion of the â€˜â€˜technicalâ€™â€™ traders in the

model strengthens the price oscillations. This result can be easily

interpreted. If â€˜â€˜technicalâ€™â€™ traders decide that price is going to fall,

they sell and thus decrease demand. As a result, price does fall and

the â€˜â€˜chartistâ€™â€™ mood of â€˜â€˜regularâ€™â€™ traders forces them to sell. This

suppresses price further until the â€˜â€˜fundamentalistâ€™â€™ motivation of

1.08

1.06

1.04

1.02

Price

1

0.98

0.96

nT = 0

nT = 0.005

0.94

Time

0.92

1 5 9 13 17 21 25 29 33 37 41 45 49

Figure 12.3 Price dynamics for the technical strategy (12.4.10) for

a Â¼ g Â¼ d Â¼ n Â¼ 1 and b Â¼ 4 with initial conditions nÃ¾(0) Â¼ 0.4 and p(0)

Â¼ 1.05.

141

Agent-Based Modeling of Financial Markets

â€˜â€˜regularâ€™â€™ traders becomes overwhelming. The opposite effect occurs

if â€˜â€˜technicalâ€™â€™ traders decide that it is time to buy: they increase

demand and price starts to grow until it notably exceeds its funda-

mental value. Hence, if the â€˜â€˜technicalâ€™â€™ traders are powerful enough in

terms of trading volumes, their concerted action can sharply change

demand upon â€˜â€˜technicalâ€™â€™ signal. This provokes the â€˜â€˜regularâ€™â€™ traders

to amplify a new trend, which moves price in the direction favorable

to the â€˜â€˜technicalâ€™â€™ strategy.

12.4.4 THE BIRTH LIQUID MARKET

OF A

Market liquidity implies the presence of traders on both the bid/ask

sides of the market. In emergent markets (e.g., new electronic

auctions), this may be a matter of concern. To address this problem,

the basic model (12.4.1)â€“(12.4.7) was expanded in the following way

[19]

dnÃ¾ =dt Â¼ vÃ¾Ã€ nÃ€ Ã€ vÃ€Ã¾ nÃ¾ Ã¾ SRÃ¾i Ã¾ rÃ¾ (12:4:11)

dnÃ€ =dt Â¼ vÃ€Ã¾ nÃ¾ Ã€ vÃ¾Ã€ nÃ€ Ã¾ SRÃ€i Ã¾ rÃ€ (12:4:12)

The functions RÃ†i (i Â¼ 1, 2, . . . , M) and rÃ† are the deterministic and

stochastic rates of entering and exiting the market, respectively. Let us

consider three deterministic effects that define the total number of

traders.6 First, we assume that some traders stop trading immediately

after completing a trade as they have limited resources and/or need

some time for making new decisions

RÃ¾1 Â¼ RÃ€1 Â¼ Ã€bnÃ¾ nÃ€ , b > 0 (12:4:13)

Also, we assume that some traders currently present in the market will

enter the market again and will possibly bring in some â€˜â€˜newcomers.â€™â€™

Therefore, the inflow of traders is proportional to the number of

traders present in the market

RÃ¾2 Â¼ RÃ€2 Â¼ a(nÃ¾ Ã¾ nÃ€ ), a > 0 (12:4:14)

Lastly, we account for â€˜â€˜unsatisfiedâ€™â€™ traders leaving the market.

Namely, we assume that those traders who are not able to find the

trading counterparts within a reasonable time exit the market

142 Agent-Based Modeling of Financial Markets

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