牛熊證與股價指數間線性和非線性關聯性

Linear and nonlinear relations between CBBC and stock index

李重叡(Chung-Jui Li)

指導教授 ： 李瑞琳

朝陽科技大學/管理學院/財務金融系/碩士(2015年)

摘要

本研究旨在探討台灣股市的牛熊證(Callable bull / bear contracts, CBBC)和台灣加權股價指數間線性和非線性關聯性。結果發現牛證和標的指數報酬間相關係數大致上為顯著正相關，這樣的結果支持標的指數上漲或下跌均和牛證漲跌有強烈地正相關。另一方面，熊證和標的指數報酬僅有少數為顯著反向關係。整體而言，牛證與標的指數具有同向變動，而熊證與標的指數具有相反方向變動。另外在牛熊證和標的指數報酬間非線性因果關係中發現無論單位半徑為1.0或1.5以及假設落後期數為從1至4，標的指數上漲或下跌均和牛證漲跌有強烈地正相關。另一方面，標的指數對熊證報酬僅有少數為顯著反向關係。整體而言，標的指數對牛證大多具有同向變動，而熊證與標的指數具有相反方向變動。

關鍵字

非線性 ； 線性 ； 牛熊證

並列摘要

This study investigates linear and non-linear relations between the Taiwan stock market CBBC (Callable bull / bear contracts, CBBC) and Taiwan Weighted Stock Price Index. We find that significant positive correlation between Bull and the underlying index returns, supporting that, Bull securities are up (down) as the underlying index rises (falls). On other hand, several results are found when observing linear relation between Bear securities and the underlying index returns. We further examine nonlinear causalities between CBBC (Callable bull / bear contracts, CBBC) and Taiwan Weighted Stock Price Index. We show that nonlinear bidirectional causalities between CBBC and Underlying Index returns. It implies friction cost in the warrant calls and puts as well as stock markets. Our findings could shed valuable insights on nonlinear causalities between CBBC (Callable bull / bear contracts, CBBC) and Taiwan Weighted Stock Price Index.

並列關鍵字

CBBC ； linear ； nonlinear

參考文獻

Black, F. and M. Scholes (1973). The valuation of options and corporate liabilities. Journal of Political Economy 81, 637-659.

Boyle, P. P. (1988).A lattice framework for option pricing with two state variables.Journal of Financial and Quantitative Analysis 23 March 1-12

Cox, J.,S.A Ross and M.Rubinstein(1979). Option pricing: a simplified approach.Journal of Financial Economics7,229-264

David A. Dickey,Wayne A. Fuller(1979)Distribution of the Estimators for Autoregressive Time Series With a Unit Root 427-431

Denker, M. and G. Keller, (1983), “Rigorous Statistical Procedures for Data from Dynamical Systems,” Journal of Statistical Physics, 44, 67-93.