臺灣博碩士論文加值系統

可轉換債券同時包含了債券及股票的特色，為目前愈來愈受歡迎之衍生性金融商品。因為它多樣的特性而增加了可轉換債券評價之難度。Chambers和Lu提出一個精確的二項因子可轉換債券評價樹。此評價樹演算法之時間複雜度為相對較高的O(n3)。
　　本篇論文我們實作Chambers和Lu的評價樹於中央處理器(CPUs)及圖形處理器(GPUs)上。程式利用了圖形處理器強大的平行處理運算能力及高記憶體頻宽。數據結果顯示在圖形處理器上之執行時間比在中央處理器上快了數倍，尤其當n大於1000時，差異更為明顯。在圖形處理器上之評價結果並且可和中央處理器上一樣準確。我們現在可於Chambers和Lu的評價樹上更加快速獲得可轉換債券的價格，並且不犠牲其精確度。

Convertible bonds are now popular derivatives
which incorporate the features of bonds and equities.
It is difficult to price convertible bonds with their various features. Chambers and Lu propose an accurate two-factor tree model for convertible bonds pricing.
The time complexity of that algorithm is the relatively high O(n^3).

In this thesis, we implement Chambers and Lu''s tree model on GPUs and CPUs. The code exploits GPUs'' computational power in parallel processing and high memory bandwidth.
The numerical results show that the execution time on GPUs is several times faster than on CPUs, especially with n > 1000. The pricing results on GPUs are also as accurate as on CPUs. We can now obtain convertible bonds'' price much faster with Chamber and Lu''s model without sacrificing accuracy.

1 Introduction 7
2 Convertible Bonds 9
2.1 Convertible Bonds Overview . . . . . . . . . . . . . 9
2.2 Benefits of Convertible Bonds . . . . . . . . . . . . 11
2.3 Risks of Convertible Bonds . . . . . . . . . . . . . .14
3 Convertible Bonds Pricing Model 17
3.1 Literature Review . . . . . . . . . . . . . . . . . . 17
3.2 Traditional Tree Models . . . . . . . . . . . . . . . 18
3.3 Chambers and Lu''s Tree Model . . . . . . . . . . . . .21
3.4 Our Implementation Methodology . . . . . . . . . . . .27
4 GPU Implementation 31
4.1 CPU and GPU Comparison . . . . . . . . . . . . . . . .32
4.2 Chambers and Lu''s Model on GPU . . . . . . . . . . . .35
5 Numerical Results 41
5.1 Implementation Results of the Chambers and Lu''s Tree Model . . . . 43
5.2 Performance of GPU Implementation . . . . . . . . . . 46
5.3 Discussions . . . . . . . . . . . . . . . . . . . . . 51
6 Conclusions 55

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