以極端值理論設計台股指數選擇權結算保證金之研究

Extreme Value Theory and the Setting of Clearing Margins on the Stock Index Option in TAIFEX

周建新(Jian-Hsin Chou) ； 陳振宇(Zhen-Yu Chen) ； 蔡雲香(Yun-Hsiang Tsai)

《輔仁管理評論》 14卷3期 (2007/10) Pp. 67-90

摘要

本文旨在應用極端值理論來設計台股指數選擇權之結算保證金，為克服樣本數不足將影響極端值分配的近似效果及參數估計的精確度，本文以日內5分鐘大盤指數報酬資料為研究標的。在研究方法上，本文利用高斯－牛頓法，來求解非線性最小平方法中的參數估計值，同時針對7種不同之極值取樣的交易時段數，在不同之違約機率下，設計台股指數選擇權之保證金水準。實證結果發現，大盤指數報酬分配呈現厚尾的Fréchet分配；另外在涵蓋99.7%價格波動下，取樣交易時段數目，若設定在90~180之間，利用極端值理論所估計出的理論保證金水準，將與實際之平均保證金水準(5.20%)，差異最為接近。

關鍵字

指數選擇權 ； 結算保證金 ； 極端值理論 ； 高斯－牛頓法

並列摘要

This paper applies the extreme value theory to set the appropriate clearing margin on the stock index opt ion trading in TAIFEX. In order to overcome the problem caused by insufficient extreme value samples that may affect the approximation results and parameter's estimation accuracy in the distribution of extreme values. We use the 5 minutes intra-day returns of weighted stock index as the research target and employ the Gauss-Newton method to estimate the parameters in the nonlinear least square model, we then estimate the appropriate margin levels according to seven trading periods (n) and different default probability. The empirical results show that the returns of weighted stock index price follow a Fréchet extreme value distribution with fat tail characteristic. Besides, in order to cover 99.7% price fluctuation, if we set the trading periods (n) between 90 to 180, then the theoretical margin level will closely follow the actual margin level (5.20%).

並列關鍵字

stock index option ； clearing margin ； extreme value theory ； Gauss-Newton method

參考文獻

Bernake, B.(1990).Clearing and Settlement During the Crash.Review of Financial Studies.3,133-151.

Booth, G. G.,Broussard, J. P.,Martikainen, T.,Puttonen, V.(1997).Prudent Margin Levels in the Finnish Stock Index Market.Management Science.43,1177-1188.

Boothe, P.,Glassman, P. D.(1987).The Statistical Distribution of Exchange Rates.Journal of International Economics.22,297-319.

Brennan, M. J.(1986).A Theory of Price Limits in Futures markets.Journal of Financial Economics.16,213-223.

Broussard, J. P.(2001).Extreme Value and Margin Setting With and Without Price Limits.The Quarterly Review of Economics and Finance.41,365-385.