SPAN跨商品價差折抵參數估計之理論與實證

SPAN Parameter Estimation for Inter-commodity Spreads: Theory and Empirical Evidence

SPAN保證金系統是目前全球最通用的含選擇權與期貨的整戶保證金應收系統，主要誘因是採用SPAN可以讓投資者的資金發揮更大的操做空間，其中最重要的原因之一是SPAN系統考慮到跨商品間的價差折抵，以避免超收應收保證金，進而造成資金效率降低。然而採用SPAN的單位必須自行估計跨商品間價差折抵率與Delta耗用比率兩項參數。Delta耗用比率之估計通常都使用合約的價值比率，本研究推導出Delta耗用比率的合理估計公式，提出以保證金比率來估計Delta耗用比率的新公式，並分別根據利率期貨與非利率期貨做跨商品價差折抵Delta耗用比率之試算。根據CME與TAIFEX的股指期貨實際價格資料做新舊Delta耗用比率的估算並做回溯測試比較，本文發現用保證金調整的新Delta耗用比率，在同樣的遮蓋率下比傳統的價值比率之估計可以讓SPAN的使用者達到更高的資金使用效率。

SPAN margin system is currently the world's most popular margin system adopted by most of exchanges that trade futures and option contracts. The main advantage of SPAN is its greater fund efficiency within the system without security compromise. One of the reasons that SPAN can save margin requirements is SPAN allows Margin credit for offsetting positions between correlated products, i.e., inter-commodity spread. To properly make use of intercommodity spread, clearing houses that adopt SPAN must estimate two important parameters: Delta ratio and spread credit rate. Most clearing houses (including TAIFEX) use contracts value ratio as the basis for delta ratio. We review the theoretical basis for estimating delta ratio and derive a new delta ratio estimation method that takes into account of the underlying margin requirements ratio between the two spread commodities. We further derive the delta ratio estimated formula for non-interest and interest rate derivative products. The new and old estimation methods for delta ratio are tested using stock index futures prices data from CME and TAIFEX to conduct a back test for inter-commodity spreads. We find that given a fixed coverage ratio, the new estimation method for delta ratio can achieve higher margin efficiency for SPAN users.