美國股市小數化對指數期貨定價誤差之影響

Abstract

本文使用日內資料（intraday data）探討美國證券交易所於2001年1月29日縮小升降單位（Decimalization，又簡稱為小數化）至0.01美元的政策，對小型S&P 500 指數期貨(E-mini S&P 500 index futures)和小型Nasdaq 100指數期貨(E-mini Nasdaq 100 index futures)的定價誤差（mispricing）之影響，並探討影響指數期貨定價誤差的因素。實證資料分為下列四組時間序列：(1) S&P 500指數現貨與E-mini S&P 500指數期貨；(2) SPDRs與E-mini S&P 500指數期貨；(3) Nasdaq 100指數現貨與E-mini Nasdaq 100指數期貨；(4)QQQ與E-mini Nasdaq 100指數期貨。本文以考慮異質變異之自我迴歸模式，參考Kurov and Lasser（2002）所選定的變數，來分析探討小數化、現貨指數波動性、期貨交易次數及離期貨到期天數等變數對定價誤差的影響。實證結果發現彙整如下：(1)以指數現貨求算指數期貨理論價格的組別，小數化對期貨定價誤差具有顯著的影響且為負效果，亦即小數化後，定價誤差明顯減少。支持本文的假說一及假說三；(2)以ETFs求算指數期貨理論價格的組別，小數化對E-mini S&P 500指數期貨的定價誤差有顯著的負效果，支持假說二；但E-mini Nasdaq 100指數期貨的定價誤差在小數化後反而顯著增加，與預期不符。(3)整體而言，指數現貨波動性愈大或離期貨到期天數愈長，則指數期貨定價誤差顯著愈大，而交易次數愈多，則指數期貨定價誤差顯著愈小。以ETFs求算指數期貨理論價格的組別有較例外的情況。

This paper examines the impact of the decimalization policy of stock market on January 29, 2001 on the mispricing of E-mini S&P 500 index futures and E-mini Nasdaq 100 index futures. It also probes into the factor influencing the mispricing of index futures. Observations obtained from intraday S&P 500 and Nasdaq 100 E-mini futures transactions and index value data is divided into the following four groups of time series: (1) S&P 500 index stock and E-mini S&P 500 index futures; (2) SPDRs and E-mini S&P 500 index futures; (3) Nasdaq 100 index stock and E-mini Nasdaq 100 index futures; (4) QQQ and E-mini Nasdaq 100 index futures. This paper considering the selected variables of Kurov and Lasser (2002), involving decimalization, the volatility of stock index, futures traded numbers, and the days leave expiration day. The results are as follows: (1) the groups that calculate the future theory price by using stock index price, decimalization has significant negative effect on index future mispricing. It support hypothesis one and hypothesis three of this paper; (2) the groups that calculate the future theory price by using ETFs price, decimalization has significant negative effect on the mispricing of E-mini S&P 500 index futures. It support the hypothesis two; but the mispricing of E-mini Nasdaq 100 index futures increases apparently instead after the decimalization, it doesn’t accord with expectation. (3) Overall, the higher volatility of stock index and the more days leave expiration day, then the index futures mispricing is apparent larger, and the more futures traded numbers, the index futures mispricing is significant smaller. However, there are some exceptions in the groups that calculate the future theory price by using ETFs price.