臺灣博碩士論文加值系統

本文利用數值積分法快速而精確的評價離散式雙障礙選擇權。在這方法之中，兩次觀察期之間只需進行一次運算，使計算速度能大幅提升。準確度也因節點能精確的放置在障礙上而有顯著改善。最後，這個方法也能處理許多特殊的狀況，例如移動式障礙或是當起始價格非常接近障礙時。這些優點使得本方法成為現有方法的重要補充。

This thesis develops a fast and accurate quadrature method for pricing discrete double-barrier options. In this method, discrete barrier options are valued with only one time step between observations, resulting in significant improvement in speed. Accuracy is greatly enhanced by allowing nodes to be placed exactly on the barriers. Finally, the flexibility of the method makes it capable of dealing with additional features, such as moving barrier or even when the initial price is very close to the barrier (the so-called barrier-too-close problem). All these merits make the method an important addition to the existing tools.

1 Introduction
1.1 Setting the Ground . . . . . . . .. . . . . . 6
1.2 Structure of the Thesis. . . . . . . . . . . . 8

2 The Quadrature Method
2.1 The Building Block of the Quadrature Method 9
2.2 Illustration with Vanilla Calls. . . . . . . 10

3 Pricing Discrete Barrier Options
3.1 Pricing Discrete Single-Barrier Options . . 14
3.2 Pricing Discrete Double-Barrier Options . . 17

4 Numerical Results. . . . . . . . . . . . . . . . . 20

5 Conclusion. . . . . . . . . . . . . . . . . . . . . 28

Appendix A. . . . . . . . . . . . . . . . . . . . . . 29

Appendix B. . . . . . . . . . . . . . . . . . . . . 31

Bibliography. . . . . . . . . . . . . . . . . . . . 33

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