自從Black & Scholes Theory誕生之後，不少針對選擇權定價理論的研究不斷誕生，隨著電腦技術以及數學理論發展漸趨成熟，定價方式也越趨精準，其中以Heston Model最為學界以及實務界重視。在執行Heston Model評價之前，我們必須先進行參數校準，設定好之後再進行蒙地卡羅模擬定價商品，而本篇研究著重在參數校準的過程與方法，透過調整誤差函數將誤差逐漸縮小，另外也檢驗參數穩定度，來看說參數是否會隨著市場資訊的影響而改變。 而在蒙地卡羅的部分，我們嘗試將標的資產的模擬次數跟時間間隔做切割，找出最有效率的模擬方法，一來減低模擬時間，二來保持評價的精準度。最後我們探討BS與Heston兩個模型的差異，發現倒在定價的部分其實相去不遠；但進一步去統計模擬的結果，Heston Model確實會受到fat tail的影響，在勝率上面確實會與BS有差別。 ;After Black & Scholes Theory born, people from business and academic fields were devoting to fix the flawless and implement BS Model in a more practical way. With well-developed mathematics theories and high-efficient computers, the ways we pricing are more accurate than it was, especially Heston Model. In Heston Model, we have to do parameters calibration before Monte-Carol simulation. In this paper, we focused on parameters calibration section and try to find a loss function that is the most accurate in calibration. Also, we examined the consistency of parameters so that we can know if parameter will be changed by information flow in the market. On the other hand, we did Monde-Carol simulation by different time space to find out the most efficient simulation step. Last but not the least, we made a comparison between BS Model & Heston Model to search if there is any difference between those two popular option pricing theories. The big discovery is that the winning probability of BS and the winning probability of Heston are not the same because of the basic assumption.
