假如金融市場上的股價（stock）走勢跟隨Heston 模型，則
可以藉由股價資料來推估參數，而若引進選擇權（option）的資
料，來處理觀察不到的波動度，也可以由股價跟選擇權的資料推
估參數。在這篇論文裡我們有兩種方法去推估參數：方法一是只
有股價資料時，這時候假設波動度（volatility）是可以觀察到的；
方法二是當波動度是觀察不到時，我們選用選擇權資料利用轉換
來代替觀察不到的波動度去推估參數。因此我們想知道上述兩種
參數估計的差距。本文使用最大概似估計法（maximum likelihood
estimator, MLE）來驗證。也利用蒙地卡羅模擬以及有母數拔靴
(parametric bootstrap) 重複抽樣方法去比較兩者的結果是否一
致。

In this paper, we want to know if the financial market stock
price trend to follow Heston model, we can estimate the parameters
by stock price data when the volatility is assumed to be observable,
and while the volatility does not observed, we can use option data to
deal with that, then use stock and option data to estimate the
parameters. In this paper, we have two methods to estimate the
parameters: one method only stock information, the assumption that
volatility is to be observed; method 2 is the assumption that
volatility is not observable, we use options data instead of using
conversion can not see the volatility to estimate the parameters. We
would like to know the difference between the estimation accuracy
of the theoretical exact value. In order to count the value of this
theory, we use the maximum likelihood estimator(MLE) to estimate
the parameters of the stochastic volatility model in the consistency
of MLE estimation. We also use the Monte Carlo simulation and the
papametric bootstrap method of repeated sampling to compare the
results.

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