a study of the impact of signal distortions on the behavior of internal traders

1、<p>　　A Study of the Impact of Signal Distortions on the Behavior of Internal Traders</p><p>　　Abstract. In this paper was based on Kyle （1985） model， considering the conduction problem of the value of

2、internal information， and established a single term insider trading by trading model to consider the case of signal distortions for the true value of the risky assets. And studied the effect of internal information has o

3、n the nature of internal trading strategies and market under a more general assumption condition. And compare the conclusion with Kyle （1985） model. </p><p>　　Key words： insider trading， rational expectation

4、s equilibrium of the value signal noise， Kyle model </p><p>　　1.Introduction </p><p>　　Every day， a large number of assets by investors trading the financial markets， these assets include stocks

5、， bonds， warrants or financial derivatives. And investors expected future income trading assets according to available information to make a judgment. This information will not only affect the behavior of the traders but

6、 also affect the price of the asset. Internal information has a significant impact on prices of trading asset， and has not been made public. Insider trading refers to the be</p><p>　　The early studies focuse

7、d on the impact of insider trading for the effectiveness of the financial market. Kyle （1985）， as the most representative literature， analyzed the situation of a risk-neutral internal traders and market makers， as well a

8、s more than unwitting noise traders. Back （1992） from the extension of the continuous-time framework， Holden and Subrahmanyam （1992）， the angle of the game from multiple internal trader behavior analysis， and Back， Cao a

9、nd Willard （2000） made Holden and Su</p><p>　　The construction of China's capital market began in the 1990s， therefore， the domestic research on insider trading began in the late 1990s， and mainly focuse

10、d on the legal and institutional level， until the beginning of this century， the research focus to the economic level， the research direction is mainly the internal traders super profit， insider trading behavior of marke

11、t effectiveness and asset price fluctuations， the main method is empirical analysis， including literature representative Wa</p><p>　　The article is organized as follows： The first part is the assumptions of

12、the model； the second part is the equilibrium solution of the single-period model； the third part is concluded and the revelation. </p><p>　　2.The Model Assumption </p><p>　　It is assumed that t

13、he market is only one risk assets， transaction entities involved in the transaction with internal traders， noise traders， market makers， these three types of traders. </p><p>　　Set the flow trading risk asse

14、ts after the real value as ， follows the normal distribution with mean of and Variance of </p><p>　　. Noise trader demand for tradable risky assets ， Noise traders trading as a random， we have reason to assu

15、me that </p><p>　　follows the normal distribution with mean and Variance ， and Independent of the true value of the risky assets. Assuming internal risk-neutral traders premise in mind that the internal risk

16、-neutral traders demand for tradable risk assets. </p><p>　　At the time of this model in the internal traders cannot directly observe the real value of risky assets， only the observed value signal related to

17、 the value of risk assets， We assume that the signal has the following form： </p><p>　　In which stands for the distortion of internal information （Tradable true value of the risky assets） passed to the insid

18、er trading process for the distortion of the true value of the risky assets， the distortions generated by a random event delivery mechanism， and the true value of the risky assets. We may assume that a normal distributio

19、n meets with mean and Variance </p><p>　　and let with the true value of the asset . The correlation coefficient is a constant ， That is . Value of the signal </p><p>　　can be introduced accordin

20、g to the normal distribution of linear transformation invariance distribution with mean variance </p><p>　　normal distribution， in which the value of the signal has the same expectations， with the risk of as

21、set value fluctuations of signal transduction by the true value of the risky assets， random events. The variance and the correlation coefficient with the value of the real asset were measured. </p><p>　　In t

22、he model， the transaction can be divided into two steps： the first step， the endogenous variables True worth in order to achieve internal traders observed value of signal ， to decide on risk assets demand， at the same ti

23、me the noise traders transaction demand Achieve， but the internal traders cannot observe . Internal traders trading demand is decided by the value of the signal ， the internal traders trading demand is a function of the

24、value of the signal： . The second step， the market maker</p><p>　　According to the market maker to make the market-clearing price . Clearing price is determined by the demand for risky assets， set clearing p

25、rice is a function of the demand for risky assets： . </p><p>　　Throughout the trading， the internal traders can profit can be expressed as . Insider trading profits and risks of the assets related to the cle

26、aring price， the market maker's pricing strategy and internal traders trading strategies， internal traders in the market maker's pricing strategy will take into account the development of trading strategies. We c

27、an put the relationship between several factors expression in the following form： </p><p><b>　　and . </b></p><p>　　3.The Single-Period Model Equilibrium Solution </p><p>

28、;　　In the above model， we defined balanced as follows： </p><p>　　Balanced definition 1： In the above model， the equilibrium of the economy as a demand strategy and price， the following condition is satisfied

29、： </p><p>　　（1）， the profit maximization conditions： give the value signal </p><p>　　any value， for any other demand strategy ， </p><p><b>　?。?.1） </b></p><p&

30、gt;　　（2） The effectiveness of the market semi-strong conditions： meet the clearing price of the transaction risk assets random variables： </p><p><b>　?。?.2） </b></p><p>　　The interna

31、l traders influence the market maker in the second step of the pricing through needs strategy in the first step. Because the market maker's pricing strategy also affect the internal trader's trading profits， whic

32、h insider trading is to find a strategy， the strategy will consider the impact of the demand strategy of the pricing strategy with the market maker makes the internal transactions by traders to maximize profits. Here， we

33、 consider internal traders demand for risk assets， the nu</p><p>　　In the above model， we can prove the following theorem： </p><p>　　Theorem 1： In the above model， there is only a linear equaliz

34、er ， Has the following form： </p><p><b>　　， （2.3） </b></p><p>　　Among them， are constants， </p><p><b>　　， </b></p><p>　　Proof： Suppose there are

35、 constant so that the linear price function and Linear demand function meet： </p><p><b>　　， （2.4） </b></p><p>　　Assuming， the internal trader's trading profits can be expressed a

36、s： </p><p><b>　?。?.5） </b></p><p>　　The internal trader's profit maximization problem of the first order conditions： ， Which by assumption </p><p>　　get . In additio

37、n， the maximization problem of second-order conditions required . </p><p>　　By assuming linear form， balanced definition of market conditions of validity of the semi-strong form can be expressed as： 　?。?.6）

38、 </p><p>　　All random variables in the above equation are subordinate to the normality assumption， which can be seen as a linear regression， and know by the projection theorem that the true value of is uniqu

39、e， so we have： </p><p><b>　　， </b></p><p><b>　?。?.7） </b></p><p>　　From the relationship between and the second-order condition derived from the above we can

40、 </p><p>　　get . To make this expression meaningful， there </p><p>　　must be . Under this condition， </p><p>　　By Theorem 1， the equilibrium pricing strategy and the risk assets dem

41、and strategy are decided by exogenous variables </p><p><b>　　. </b></p><p>　　4. Conclusions and Revelation </p><p>　　Model results contrast with Kyle （1985）， we can see

42、a balanced trading strategy of the proposed model endogenous variables becomes a （This is because the internal transactions of people in the present model can no longer be observed directly to the true value of the risky

43、 assets ， but merely the value of the signal can be observed）. Meanwhile， we can calculate in the Kyle （1985） model or in the present model， there is </p><p>　　， which means that in the model， is </p>

44、<p>　　Insider trading on the demand for risky assets coefficients that measure the internal trading behavior of traders for the market attack. In this article coefficient expression </p><p>　　added new

45、 exogenous variables ， and is easy to see that in the case given the exogenous variables， in this article， the coefficient is significantly greater than Kyle （1985） model of insider trading on the demand for risky assets

46、 coefficient values. Instructions， taking into account the true value， the value of the signal distorted when the internal traders trading behavior offensive by the extent of the impact of fluctuations in signal distorti

47、ons， and in this article， the model assumes that un</p><p>　　Value increased， i.e. when the degree of fluctuation of the signal distortion is deepened， the internal transaction's attack enhanced， and an

48、enhanced degree of is not a linear relationship with the degree of signal distortion fluctuation growth. </p><p>　　Value information generating random events of the twisted portion and the true value is a po

49、sitive correlation， that is </p><p>　　when the value of the signal distortion enhanced market maker pricing strategy for the real inside information reveals. At this point， when the value signal distortions

50、part of the true value of the positive correlation between the stronger part of the random events distorted the higher the volatility， the value of the signal response of the internal information is more accurate， more a

51、ggressive trading practices internal traders， leading to market maker pricing when can get more information abo</p><p>　　is easy to see is greater than the depth of the market in Kyle （1985） model for. Visib

52、le signal distortions affect the depth of the market， of its growth and the growth of the market depth showing the nonlinear positive growth relationship. Relative to not consider the signal problem when insider trading

53、is based on the observed signal to determine the demand for current assets， while the value of the signal with the distortion of the true value of risk assets weakened insider trading relative t</p><p>　　In

54、this article to build a single-period model， when taking into account the information conduction problem， the internal traders’ unconditional expected profit will be less than the unconditional expected value of the insi

55、der trading no signal problem. This is because the internal message transfer process distorted， random fluctuations in signal distortions encourage the internal traders more transactions， and at the same time will increa

56、se the depth of the market. In this case， the more intern</p><p>　　From the above analysis， we believe that the value signal for the distortion of the internal information， which is a distortion of the true

57、value of the risky assets， will affect internal to the trading behavior and the nature of the market. According to our model assumptions about the value of the signal， we value signals distortions into the extent of the

58、impact of random part of two parts： the value of signal distortion fluctuations， and the value of signal distorting the true value of the pa</p><p>　　1.Back K. Insider trading in continuous time [J]. Review

59、of Financial Studies， 1992， 5：387- 410. </p><p>　　2.Back， K.， Cao ， H.， Willard， G（2000）： "Imperfect competition among informed traders"， Journal of Finance 55， 2117-2155. </p><p>　　3.

60、Holden C W， Subrahmanyam A. Long-lived private information and imperfect competition [J]. Journal of Finance，1992，47：247一270. </p><p>　　4.Kyle Albert S. Continuous auctions and insider trading [J]. Econometr

61、ica， 1985， 53：1315-1335. </p><p>　　5.Kyle， Albert， Albert Wang （）： "Speculation duopoly with agreement to disagree： Can overconfidence survive the market test？” ，Journal of Finance， 1997， 52： 28 2073-20

62、90. </p><p>　　6.Miaoxin Qiong Zou Hengfu： "the internal traders trading behavior analysis" [J]， world economy， 11， 2004. </p><p>　　7.Tang Qiming Zhang Gong： "based on the volume a

63、nd price of China's stock market insider trading causality analysis [J] Quantitative & Technical Economics Research， 6， 2005. </p><p>　　8.Wang Guipu： "China's stock market insider trading in