臺灣博碩士論文加值系統

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。

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.

目 錄
口試委員會審定書 ........................................................................................................... i
致 謝 ............................................................................................................................... ii
摘 要 ............................................................................................................................... iii
Abstract ............................................................................................................................ iv
圖目錄 ............................................................................................................................. vi
表目錄 ............................................................................................................................ vii
第一章 緒論 .................................................................................................................. 1
1.1研究目的與動機 .................................................................................................... 1
1.2論文架構 ................................................................................................................ 2
第二章 Hilliard和Schwartz（1996）的雙變數二元樹模型 ..................................... 3
2.1隨機波動率模型假設 ............................................................................................ 3
2.2 建構雙變數二元樹 ............................................................................................... 3
2.3 跳動幅度和聯合機率 ........................................................................................... 5
2.4 Hilliard和Schwartz（1996）演算法的問題 ....................................................... 7
第三章 雙變數2/3-元樹模型 ....................................................................................... 9
3.1 隨機波動率模型假設與轉換 ............................................................................... 9
3.2平均數追蹤法（mean-tracking method） ............................................................ 9
3.3 跳動幅度和聯合機率 ......................................................................................... 16
第四章 數值資料與分析 ............................................................................................ 19
第五章 結論與展望 .................................................................................................... 25
附 錄 .............................................................................................................................. 26
參考文獻 ........................................................................................................................ 36

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