- 學位論文
在隨機波動率下之雙變數樹評價模型
On Bivariate Lattices for Option Pricing under Stochastic Volatility Models
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摘要
Hilliard和Schwartz（1996）提出一個雙變數二元樹模型，其模型可以在隨機波動率下評價選擇權，並允許股價與波動率有相關性。本論文旨在探討 Hilliard和 Schwartz（1996）的雙變數二元樹模型演算法之缺點，以及提供一個部分修正方案。論文針對在 Hilliard和Schwartz（1996）模型中會發生錯誤機率的股價二元樹，改用平均數追蹤法建構的三元樹，而波動率還是維持二元樹，稱此架構為雙變數2/3-元樹模型，最後用此模型去評價選擇權。
並列摘要
The bivariate binomial framework of Hilliard and Schwartz (1996) allows non-zero correlation between the stochastic volatility and the underlying process. It can also be used to value American options. This thesis points out the problems with their bivariate binomial model. It also provides a partial solution to deal with those problems. When pricing options with the Hilliard-Schwartz model, it is easy to demonstrate that incorrect probabilities will occur in some situations. We use the mean-tracking method to construct trinomial trees instead of binomial trees for one dimension. Nevertheless, the stochastic volatility dimension still adopts the binomial tree as Hilliard and Schwartz (1996). The framework will be called the bivariate bino-trinomial model, and it is used to evaluate options.
參考文獻
[1] Yung-Chi Chu. Option Pricing with Stochastic Volatility. MBA thesis, NTU, 2006.
[2] Tian-Shyr Dai and Yuh-Dauh Lyuu. The Bino-Trinomial Tree: A Simple Model for Efficient and Accurate Option Pricing. Journal of Derivatives, Vol. 17 (2010), 7–24.
[3] S. Heston. A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options. The Review of Financial Studies, 6, No. 2 (1993), 327–343.
[4] J. Hilliard and A. Schwartz. Binomial Option Pricing under Stochastic Volatility and Correlated State Variables. Journal of Derivatives, Fall 1996, 23–39.
[5] J. Hull and A. White. The Pricing of Options on Assets with Stochastic Volatility. Journal of Finance, 42, No. 2 (June 1987), 281–300.
延伸閱讀
- 邱暉翔（2012）。在隨機波動率下之雙變數樹評價模型〔碩士論文，國立臺灣大學〕。華藝線上圖書館。https://doi.org/10.6342/NTU.2012.10427
- 高文洪（2011）。選擇權評價之雙變數樹狀模型建構〔碩士論文，國立臺灣大學〕。華藝線上圖書館。https://doi.org/10.6342/NTU.2011.10909
- 張凱雲（2016）。評估單因子隨機效應模型中多種單邊容許界限在非常態隨機分布下的表現〔碩士論文，淡江大學〕。華藝線上圖書館。https://www.airitilibrary.com/Article/Detail?DocID=U0002-1706201610513600
- Lin, T. W. (2021). 雙變量邏輯可滿足性的新解法與實作分析 [master's thesis, National Taiwan University]. Airiti Library. https://doi.org/10.6342/NTU202102417
- Gao, X., Deng, D., & Shan, Y. (2014). Lattice Methods for Pricing American Strangles with Two-Dimensional Stochastic Volatility Models. Discrete Dynamics in Nature and Society, 2014(), 153-158-019. https://doi.org/10.1155/2014/165259