| Summary: | 碩士 === 中原大學 === 工業工程研究所 === 92 === 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 futures
and market, which is called the basis. In this thesis, the author studies three aspects: investment application, trading strategy and implementing investment strategy. In investment application, the author assumes that the spot price and futures price follow stochastic differential equation (SDE), then studies the stochastic behavior of the corresponding basis. In trading strategy, index arbitrage is sometimes accomplished by trading a relatively small representative sample of stocks whose movements closely mirror those of the index. Consequentially, the author also reproduces a portfolio as closely as possible an index by using the CAPM model and constructs a benchmark portfolio by minimizing the tracking error of the replicating portfolio.
Furthermore, based on the underlying stochastic process, the author also determines the investment opportunity. By studying the distribution of maximums and minimums of basis, she finds two ways to execute the investment strategy, one is long the stocks underlying the index and taking a short position in futures contract portfolio of stocks and short futures and the other is doing the reverse, by that implying investment opportunities. In addition, the author compares the performance of investment strategy between model basis and empirical basis.
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