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| 研究生： |
賴瑋鎗 Wei-Chiang Lai |
|---|---|
| 論文名稱： |
選擇權定價理論以Heston Model為例 評價股權與外匯商品 Option Pricing Theory : Implementation of Heston Model for Index Options and FX Options |
| 指導教授： |
吳庭斌
Ting-Pin Wu 何中達 Chung-Da Ho |
| 口試委員: | |
| 學位類別： |
碩士 Master |
| 系所名稱： |
管理學院 - 財務金融學系 Department of Finance |
| 論文出版年： | 2016 |
| 畢業學年度： | 104 |
| 語文別： | 中文 |
| 論文頁數： | 71 |
| 中文關鍵詞： | 蒙地卡羅模擬 、選擇權定價 |
| 外文關鍵詞： | Monte-Carol Simulation, Option Pricing |
| 相關次數： | 點閱：21 下載：0 |
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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.
Hurn A.S., Lindsay K.A. and McClelland A. J. (2012), “Estimating the Parameters of Stochastic Volatility Models using Option Price Data“,working paper, School of Economics and Finance, Queensland University of Technology
Heston S. L. (1993), “A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options”,The Review of Financial Studies,6,327-343.
Melino A. and Turnbull S.M. (1990),“ Pricing Foreign Currency Options With Stochastic Volatility”, Journal of Econometrics, 45,239-265.
Rouah F. D. (2013),“The Heston Model and its Extensions in Matlab and C#”, John Wiley & Sons Inc. ,New York.
Wilmott P. (2013) ,“The Best of Wilmott 1: Incorporating the Quantitative Finance Review”, John Wiley & Sons Inc. ,New York.
