| Summary: | 碩士 === 國立臺灣大學 === 資訊工程學研究所 === 87 === . An option is a financial instrument whose payoff is based upon another, more elementary financial instrument, such as stocks or bonds. It gives its owner the right to buy or sell a particular underlying asset at a stated price within a limited time. With the rapid growth and deregulation of option market in Taiwan, more and more option products have been designed to fit investors' needs. Some people, such as hedgers, use it to hedge their risk, while others, like speculators, may intend to profit from this instrument.
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. In Taiwan, financial options appeared on Taiwan's exchange in mid-1997. Options issuers need to hedge through delta hedge. The difficulty of delta hedge with stocks and bonds is that securities houses are not allowed to short stocks. This explains why puts are never issued, because a put's delta is negative. How to create the put market is our main concern.
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. Our proposal is to issue calls and puts together. Of course, the proportion has to be right, say, 4 calls for each put. This makes the overall probability of shorting stocks smaller, and we have experimental data to back up the claim. Now assume the securities house can short stock index futures. When the stock portfolio goes into negative territory because of negative option portfolio delta, the securities house shorts the index futures. Although, the result cannot be perfect hedge, it would be much better than sitting idly.
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. In this thesis, we derive by the optimal hedge ratio
to decide how many stock index futures contracts to hold in our
hedge portfolio. When the correlation between the stock price and the stock index are high, the hedging result is very encouraging. It shows with many numerical experiments that the proposal works well.
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. A common misunderstanding of the proposal is that it is just a simple application of the put-call parity, which is the simplest way to create puts. Our proposal has nothing to do with the put-call parity at all. To use the put-call parity, the securities house which issues puts has to buy calls and, well, short stock, which it is prohibited from doing!
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