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金融商品在不同交易場所價格發現的比較:以台指期貨與現貨及新台幣匯率為例(1/2)

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行政院國家科學委員會補助專題研究計畫成果報告

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金融商品在不同交易場所價格發現的比較:以台指期貨與現貨為例

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計畫類別:;個別型計畫 †整合型計畫

計畫編號:

94-2416-H-004-051-

執行期間:

94 年 08 月 01 日 至 95 年 12 月 31 日

計畫主持人:張元晨

本成果報告包括以下應繳交之附件:

□赴國外出差或研習心得報告一份

□赴大陸地區出差或研習心得報告一份

□出席國際學術會議心得報告及發表之論文各一份

□國際合作研究計畫國外研究報告書一份

執行單位:國立政治大學財管系

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2

行政院國家科學委員會專題研究計畫成果報告

國科會專題研究計畫成果報告撰寫格式說明

Preparation of NSC Project Reports

計畫編號:

94-2416-H-004-051-

執行期限:

94 年 08 月 01 日 至 95 年 12 月 31 日

主持人:張元晨 國立政治大學財管系

一、中文摘要 摘要: 本文分析台灣現貨、期貨及選擇權市場日內 價格發現的情形,我們發現台灣的期貨交易 對台股指數價格發現最有影響,但其交易成 本較高,選擇權交易對台股指數價格發現的 影響會依據選擇權價內、價外而有差異,價 外選擇權相對其他選擇權對台股指數價格 發現較有影響,因此可以瞭解有私有資訊的 投資人對價外選擇權的高槓桿特性較為偏 好。同時我們發現價內選擇權相對其他選擇 權對台股指數價格發現較無影響,決定台股 指數價格發現的主要因素為市場的漲跌及 交易標的是否為價外選擇權。 關鍵字:價格發現,期貨市場,選擇權市 場 。

ABSTRACT: We extend the understanding

of information processing among spot, futures, and option markets to an emerging market. Based on data from Taiwan's stock, futures, and options markets, we examine the information processing role of each market paying attention to liquidity, option types, option moneyness, and market cycles. We

find that trades on futures contribute the most to price discovery but they are also the most costly in executing information trading. The informational role of options varies with moneyness and market cycles. Options are more informative during a downtrend period. Out-pf-the-money options have higher permanent price effects, greater price contributions, and larger information shares than other options, which suggests that informed traders are more concerned about an option's leverage than its delta or vega. Our results indicate that in-the-money options are less informative, and market cycles as well as option moneyness affect the informational role of options.

KEYWORDS: Price discovery, futures markets, option markets.

二、研究動機

The informational role of derivatives

markets in the price discovery process has

drawn great attention from academicians and

practitioners. Certain market structures may

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price distortions, or prone to error. It is our

interest to investigate the quality of

transaction prices among different markets

and information contained in the transaction

prices across different trading venues. We

explore the role of price discovery for

derivatives in the Taiwan markets. We

compare information contributions among the

Taiwan stock spot index (TXI), the index

futures (TXF), and the implied index price

derived from the index options (TXO). We

use the tick-by-tick and transaction data to

analyze the price discovery process under

different market cycles and option

moneyness.

三、研究方法與結果

To analyze the information role of the

three markets in the price discovery process,

we conduct the information share analysis

(Hasbrouck, 1995). The information share

analysis estimates the information share of a

market according to that market’s

contribution to the total variance of the

common random-walk component. The

information flow analysis is able to show the

portion of price discovery from different

markets and identifies the venue giving the

most informative trades.

四、參考文獻

Barclay, M. J., and J. B. Warner, 1993.

Stealth trading and volatility: which trades move prices? Journal of Financial Economics, 34, 281-305.

Bekaert, G., and G. Wu, 2000. Asymmetric volatility and risk in equity markets,

Review of Financial Studies, 13, 1-42.

Booth, G. G., R. W. So, and Y Tse, 1999. Price discovery in the German equity index derivatives markets, Journal of Futures Markets, 19, 619-643.

Booth, G. G., J.C. Lin, T. Martikainen, and Y. Tse, 2002. Trading and pricing in upstairs and downstairs stock markets, Review of Financial Studies, 15, 1111-1135.

Cao, C, E. Ghysels, and F. Hatheway, 2000. Price discovery without trading: Evidence from the Nasdaq preopening, Journal of Finance, 55, 1339-1365.

Chakravarty, S., H. Gulen, and S. Mayhew, 2004. Informed trading in stock and option markets, Journal of Finance, 58, 1235-1257.

Chan, Kam. C., Y Chang, and P. Lung, 2005. Informed trading under different market conditions and moneyness: Evidence from TXO options, Working paper, University

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Chan, Kam C., L. Cheng, and P. P. Lung, 2004. Net buying pressure, volatility smile, and abnormal profit of Hang Seng Index options, Journal of Futures Markets, 24, 1165-1194.

Journal of Business and Economic Statistics, 13, 27-35.

Hasbrouck, J., 1995. One security, many markets: determining the contributions to price discovery, Journal of Finance, 50, 1175-1199.

Hasbrouck, J., 2003. Intraday price

formation in U.S. equity index markets, Journal of Finance, 53, 2375-2399.

Holthausen, R. W., R. Leftwich, and D. Mayers, 1987. The effects of large block transactions on security prices: A

cross-sectional analysis, Journal of Financial Economics, 19, 327-368

Stoll, H. R., and R. E. Whaley, 1990. The dynamics of stock index and stock index futures returns, Journal of Financial and Quantitative Analysis, 25, 441-468.

Whaley, R., 1982. Valuation of American call options on

dividend-paying stocks: empirical tests, Journal of Financial Economics, 10, 29-58.

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Table 1

The descriptive statistics for TXI, TXF, and TXO

This table presents descriptive statistics for Taiwan index returns in one-minute interval for among the Taiwan stock spot index (TXI), the index futures (TXF), and the implied index price in the index options (TXO) . In this ex-post study, the entire sample is divided into two subperiods. Downtrend market runs from January, 2002 to April, 2003, and uptrend market runs from May, 2003 to March, 2004. We choose April 2003 as the dividing line between the downtrend and uptrend markets because the Taiwan stock index started moving up in April 2003.

Obs. Mean (10-6) Std. Min Max

Entire period (01/02/2002~03/19/2004) TXI 120,954 1.1308 0.0010 -0.0463 0.0331 TXF 120,954 1.4999 0.0012 -0.0354 0.0362 TXO 120,954 1.7370 0.0017 -0.0516 0.0413 Downtrend (01/02/2002~04/29/2003) TXI 69,692 -4.0635 0.0011 -0.0463 0.0331 TXF 69,692 -3.5682 0.0013 -0.0354 0.0362 TXO 69,692 -4.5109 0.0020 -0.0516 0.0413 Uptrend (04/30/2003~03/19/2004) TXI 51,262 8.1926 0.0008 -0.0155 0.0193 TXF 51,262 8.3902 0.0008 -0.0190 0.0274 TXO 51,262 10.2311 0.0013 -0.0234 0.0312

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Table 2

The means of the daily information shares for the TXI, TXF, and TXO

ISi = Ci2 Σii / Var(Φ) (17)

This table reports the means of lower bounds and higher bounds in the information share analysis for the equity, futures, and implied prices in options. ISi is the information share of market i and Σii is the

variance of

ε

i. The calculation is discussed in Section 4.3. This study uses minute-by-minute time intervals in conducting information share analysis. At the start of each trading day, as soon as an equity index observation is reported, the most recent trades for the futures and options markets are acquired to form the first matched price set for the first trading minute. This matched price set is saved and a new matched price set is formed in the same manner for the second minute on the trading day. To minimize the impact of data staleness on the test, we eliminate those matched price set with prices recording more than fifteen seconds apart. Information share bounds are computed each day using intraday transactions data. Since an estimate of the information share’s standard error is difficult to obtain, the analysis follows Hasbrouck and Chakravarty et al. in using daily variation in the information share to determine the statistical significance of the estimates. Because price innovations across markets are usually dependent, the information share is not uniquely defined. This study computes a range of information shares instead of a point estimate. The upper and lower bounds of this range are obtained by trying all alternative rotations in Equation (19).

TXI TXF TXO

IS mean Std. IS mean Std. IS mean Std. The entire sample period 43.86% 15.36% 46.69% 21.55% 9.46% 5.86%

The downtrend period 41.89% 17.11% 47.63% 23.06% 10.48% 6.42% The uptrend period 46.57% 13.69% 45.39% 19.72% 8.04% 5.76%

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Table 3

The means of the daily information shares for options across moneyness

ISi = Ci2 Σii / Var(Φ) (17)

This table reports the means of lower bounds and higher bounds in the information share analysis for the implied prices in options across moneyness. We define out-of-the-money (OTM) options as options with delta ranging between 0.45 and 0.02; at-the-money option (ATM) options as options with delta ranging between 0.45 and 0.55; and in-the-money (ITM) options as options with delta ranging between 0.55 and 0.98. ISi is the information share of market i and Σii is the variance of

ε

i. The

calculation is discussed in Section 4.3. This study uses minute-by-minute time intervals in conducting information share analysis. At the start of each trading day, as soon as an equity index observation is reported, the most recent trades for the futures and options markets are acquired to form the first matched price set for the first trading minute. This matched price set is saved and a new matched price set is formed in the same manner for the second minute on the trading day. To minimize the impact of data staleness on the test, we eliminate those matched price set with prices recording more than fifteen seconds apart. Information share bounds are computed each day using intraday transactions data. Since an estimate of the information share’s standard error is difficult to obtain, the analysis follows Hasbrouck and Chakravarty et al. in using daily variation in the

information share to determine the statistical significance of the estimates. Because price innovations across markets are usually dependent, the information share is not uniquely defined. This study computes a range of information shares instead of a point estimate. The upper and lower bounds of this range are obtained by trying all alternative rotations in Equation (19).

The downtrend period

ITM ATM OTM

IS mean Std. IS mean Std. IS mean Std.

Call options 0.57% 5.36% 8.59% 5.68% 7.03% 6.26%

Put options 1.21% 7.55% 11.26% 6.70% 14.62% 8.19% The uptrend period

ITM ATM OTM

IS mean Std. IS mean Std. IS mean Std. Call options 2.05% 4.24% 9.29% 6.41% 11.08% 5.45%

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參考文獻

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