基差的波動與到期日效應在投資上之研究

The Study of the Volatility with Maturity Effects in the Basis and its Application in Investments

陳榆涵(Yu-Han Chen)

指導教授 ： 張國華 ； 張國華

中原大學/工學院/工業工程研究所/碩士(2003年)

https://doi.org/10.6840/cycu200300336

摘要

近年來，許多新型態的衍生性金融商品的出現，例如期貨與選擇權，帶給投資者更多的投資方式及套利機會。其中，投資者便可以藉著觀察期貨與現貨之間的差值，即所謂的基差，來進行其投資套利。
在本研究中，我們使用隨機過程的觀念，描述指數期貨與大盤指數間基差的動態。我們假設現貨與期貨均服從SDE (Stochastic Different Equation) 此種隨機過程，進而可求得基差的動態模式。接著在基差的模式中，加入到期日效應，同時觀察有無套利機會，並配合我們的投資策略，達到獲利的目的。
在第二章中，我們會說明隨機過程在財經方面的應用。在第三章中，我們利用大盤指數及指數期貨服從SDE的特性，找出兩者之間的差值(即所謂之基差)的隨機過程，並加入到期日效應。在第四章中，對基差模型作實際的驗證，並使用我們的投資策略，觀察獲利的情形。

關鍵字

基差 ； 到期日效應 ； 隨機過程

並列摘要

In recent years, the emergence of new financial derivatives such as options and futures, provides more investment opportunities for the investor. Also due to these new instruments, investor has more abilities and opportunities to obtain the sure profits. One such opportunity can be observed from the difference between the future and market, which is called the basis.
In this thesis, we consider the index future and study the stochastic behavior of the corresponding basis. We assume that the spot price and future price follow stochastic differential equation (SDE) and we derive the stochastic process of the ratio of the future price and the spot price. With the maturity effect taking into account, we define the important parameters for the process. Furthermore, based on the underlying stochastic process, we also define the arbitrage opportunity.
By using our basis model, we can find the arbitrage opportunities from the relation between the remaining time to maturity of the future contracts and the basis. Then we executed our investment strategy by that implying arbitrage opportunities.

並列關鍵字

Basis ； Maturity effect ； Stochastic differential equation (SDE) ； Arbitrage.

參考文獻

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