| Summary: | 碩士 === 國立臺灣大學 === 資訊工程學系 === 86 === This thesis aims to test the market efficiency and see if there is any arbitra
geopportunity in Taiwan''s option market. If the opportunity exists, we ask how
we can take advantage of it to earn riskless profits. We compare most of the
options issued, from the viewpoint of the issuer to see if it can make money f
rom the market. For volatile stocks, it is better to incorporate implied volat
ility into hedging than using historical volatility only. Besides, if the opti
on is issued when the underlying stock price is relatively low, one can easily
meet the requirement of hedging and even make money. In the process, we intro
duce an idea that can greatly speed up the calculation of the implied volatili
ty of American option. It is the concept of differential tree. With this techn
ique, the running time can be reduced to O(n^2) and the space to O(n), where n
is the number of time periods. The results are very encourging. For example,
problems with several hundreds of periods can be solved in milliseconds on a t
ypical personal computer. Even trees with up to 1000 periods can be calibrated
within 1.32 seconds.
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