實物商品便利殖利率之估計與動態路徑的配適

本文沿用Lin and Duan (2005)所採用之便利殖利率持有成本與買權模型來估算實物商品之便利殖利率，研究對象包含貴重金屬、能源商品與金融債券等三類，分別包含黃金、白銀、天然氣、無鉛汽油、10年期美國國庫券與30年期美國國庫券等6種商品。本文除了估算便利殖利率外，更藉由現貨價格與期貨價格的波動與便利殖利率之關係，以驗證Samuelson (1965)假說。最後本文運用了GARCH(1，1)、GARCH(1，1)-M及EGARCH(1，1)等三種模型來配適便利殖利率的走勢，並比較模型之配適程度。實證結果發現，以買權模型所估算之實物商品便利殖利率皆大於持有成本模型所估得；實證結果亦發現，便利殖利率之期間結構多呈上升型態，與理論是一致的。在驗證Samuelson (1965)假說上，大部分貴重金屬與能源類商品皆符合其假說，即當便利殖利率處於低檔時，表示存貨位於高水準，此時現貨價格變動幅度與期貨價格波動幅度一致；當便利殖利率處於高檔時，表示存貨位於低水準，此時現貨價格波動幅度將大於期貨價格波動幅度。最後我們發現，貴重金屬與能源類之便利殖利率，以GARCH(1，1)與GARCH(1，1)-M模型配適效果較佳，且以GARCH(1，1)-M的配適結果相對最佳。

關鍵字

實物商品；便利殖利率；持有成本模型；一般化自我迴歸條件異質變異數模型

並列摘要

In this study, we use the cost-of-carry model and call options model to estimate convenience yields, which advanced by Lin and Duan (2005). The sample of the study includes three kind’s markets which are precious metal, energy and finance markets, and includes gold, silver, natural gas, gasoline, 10 year U.S. treasury notes and 30 year U.S. treasury bonds etc. Besides estimating the convenience yields, we also observe the relationship between the volatility of spot prices and future prices to test the hypothesis of Samuelson (1965). Finally, we use GARCH (1, 1), GARCH (1, 1)-M and EAGRCH (1, 1) models to fit the path of estimated convenience yields and compare which one is better. The results show that the value of convenience yields estimated from call options model are higher than the cost-of-carry model. The term structure of convenience yields presents an upward sloping which is consistent with the storage theory. In testing the hypothesis of Samuelson (1965), the results show that at high inventory level, spot and futures prices have roughly the same variability, resulting in lower convenience yield; at low inventory level, spot prices of crude oil vary more than futures price, resulting in higher convenience yield. These results are consistent with Samuelson (1965) hypothesis. Finally, we find that both GARCH (1, 1) and GARCH (1, 1)-M can fit the path of convenience yields, and GARCH (1, 1)-M is the best.

並列關鍵字

Commodities ； Convenience Yield ； Cost-of-Carry Model ； GARCH

參考文獻

1. Ahmet, E., 2004, ”Optionality and Daily Dynamics of Convenience Yield Behavior : An Empirical Analysis.” Journal Of Financial Research 1, 143-158.

2. Bollerslev, T., 1987, “A Conditional Heteroskedastic Time Series Model for Seculative Prices and Rates of Return.” Review of Economics and Statistics 69, 542- 547.

5. Carmona, R. and M. Ludkovski, 2004, “Spot Convenience Yield Models for the Energy Markets.” In Mathematics of finance 351, 65–79.

6. Casassus, J. and P. Collin-Dufresne, 2005, “Stochastic Convenience Yield Implied from Commodity Futures and Interest Rates.” Journal of Finance 60, 2283-2332

8. Fama, E. and K. French, 1988, “Business Cycles and the Behavior of Metals Prices.”Journal of Finance 43, 1075-1093.

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實物商品便利殖利率之估計與動態路徑的配適

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