本研究分析且改良結合對角模型與SPAN保證金邏輯之組合式保證金系統Beta-Simulation，來計算傳統方式難以處理之包含股票指數期貨合約、個股與個股選擇權的投資組合。Beta-Simulation系統有別於其他保證金系統概念，以個股過去的歷史beta來簡化跨商品折抵的保證金估算，因此Beta-Simulation在計算過程上不僅比SPAN來的容易，也比TIMS系統在單一個股選擇權的跨商品風險估算上更具理論基礎。
本文以美國市場的資料來對Beta-Simulation系統進行模擬部位測試。測試結果顯示新的保證金系統在市場風險中提供了與SPAN相同的保障，但在擔保保證的要求上卻比SPAN系統來的要少。而另一現行的個股選擇權保證金系統TIMS，在美國市場的資料測試下，其保證金在安全性表現上就沒有SPAN與Beta-Simulation來的優秀。因此，Beta-Simulation是用於計算保證金需求與衡量含股票類衍生性商品投資組合風險上之較佳風險估算模型。
此外，我們更以台灣期貨交易所中，全體投資人實際未平倉部位之投資組合資料對Beta-Simulation系統做市場實際投資人操作部位測試。實證結果發現， Beta-Simulation系統確實改進了SPAN與TIMS面臨跨商品交易之風險折抵問題並有效降低資金成本，不但保證金需求平均只有TAIFEX之SPAN保證金的74%，也可給予與SPAN同樣的保護。而Beta-Simulation系統也通過了壓力測試，在市場價格劇烈變動時，Beta-Simulation系統仍可以確實地捕捉投資人在實際市場波動下所面臨之風險而提供有效的風險衡量與保護。

We modified the popular SPAN margining model with a diagonal model to construct a margining system called Beta-Simulation. We use Beta-Simulation to calculate margin requirements for portfolios that include stock index futures contract, stocks, and stock options. The Beta-Simulation system uses historical stock beta to simplify setting the appropriate requirements for collateral offset estimates for inter-commodity spreads. Our model performs computational procedure more easily than SPAN and offers a sounder theoretical basis than TIMS for credit offset estimates among individual stock options.
The Beta-Simulation model back tests competing systems using data from U.S. markets. The test results show that the new margining system provides the same market risk protection as the SPAN system but with collateral levels that are substantially less than those required by SPAN. Other popular margining systems for stock options TIMS cannot provide the same coverage for U.S. market data. Therefore, the Beta-Simulation system is shown to be a better model of calculating margins requirements and for measuring risk with respect to portfolios containing stock derivatives.
We also test the Beta-Simulation model empirically using all actual open positions by the Taiwan Futures Exchange’s clearing members. The back tests show that the new model requires only 74% of the TAIFEX SPAN margin requirements to offer the same protection at the same confidence interval. Our model also passes the simulated stress test by being assessed against the period when the financial tsunami swept the world.

謝 誌 i
摘 要 ii
Abstract iii
Table of Contents iv
List of Figures v
List of Tables vi
1. Introduction 1
2. Literature Review 6
2.1. SPAN Overview 8
2.2. TIMS Overview 10
3. Theoretical Model 13
3.1. Beta-Simulation Model 13
3.2. Calculation Procedure of Beta-Simulation 15
3.2.1. Estimate the Systematic Risk of the Entire
Portfolio 15
3.2.2. Estimate the Non-Systematic Risk of the Entire
Portfolio 16
3.2.3. Estimate the Total Risk of the Entire
Portfolio 16
3.3. Methods of Comparing Different Margining
Systems 17
4. Empirical Test Results for Comparison Margin
Systems 21
4.1. Data from U.S. Markets 21
4.2. Empirical Test in U.S. Markets 23
4.3. Data from Taiwan Markets 37
4.4. Test Results Using Actual Position Data in Taiwan
Markets 38
4.4.1. Comparison of Margin Requirements under
Beta-Simulation and SPAN 38
4.4.2. Back Test 41
4.4.3. Stress Test 44
4.5. Causes of Margin Shortfall 46
5. Application 48
5.1. Data 49
5.2. The Beta-Simulation Test Result for Size of
Clearing and Settlement Funds 49
5.3. The SPAN Test Results for the Size of Clearing and
Settlement Funds 53
5.4. Summary 54
6. Conclusions and Suggestions 56
References 58
Appendix 60

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