臺灣博碩士論文加值系統

知情交易率(Probability of informed trading, PIN)被廣泛用於衡量證券市場上的資訊不對稱。傳統上，PIN模型是通過最大概似估計(Maximum Likelihood Estimation, MLE)結合期望最大化(Expectation-Maximization, EM)演算法來進行估計的。然而，該模型的假設是，在給定資訊情境下，買入和賣出交易次數之間的相關性是獨立的，但實證資料不支持此假設。為此，我們提出了一種使用copula函數來評估具有相關性結構的PIN模型的方法，通過基於copula的聚類方法結合期望條件最大化(Expectation Conditional Maximization, ECM)演算法。本文不僅推廣了PIN模型，還提供了一種評估買入和賣出交易次數之間相關性的新觀點。

Probability of informed trading (PIN) is widely used to determine the information asymmetry in the security market. Traditionally, the PIN model is estimated by the maximum likelihood estimation (MLE) via expectation-maximization (EM) algorithm. However, the model assumption conclude that the correlation between buys and sells are independent, which seems not reasonable in empirical financial market. We proposed a method to evaluate the PIN model with the correlation structure by using the copula function. Though the copula-based clustering method with expectation conditional maximization (ECM) algorithm. This paper not only generalized the PIN model but also give a new view to evaluate the correlation between buys and sells.

摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1 PIN Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Copula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.3 ECM Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.4 Computational Issue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.4.1 Continuous marginal . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.4.2 Discrete marginal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.1 One example with model selection . . . . . . . . . . . . . . . . . . . . . . . . 16
3.2 Large scale experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4 Real data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.1 Stock AAPL in 2008 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.1.1 Poisson marginal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.1.2 Zero-inflated Poisson marginal . . . . . . . . . . . . . . . . . . . . . . 27
4.2 Stock NTE in 2008 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.2.1 Poisson marginal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.2.2 Zero-inflated Poisson marginal . . . . . . . . . . . . . . . . . . . . . . 30
5 Discussion and Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
Appendix A Real data fitting results . . . . . . . . . . . . . . . . . . . . . . . . . . 37

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