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.
