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題 名 | 降低因數值方法所引起的誤差--以常態分配為例=How to Reduced the Error Induced by Numerical Computation |
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作 者 | 朱正民; 楊雪蘭; | 書刊名 | 中州學報 |
卷 期 | 22 民94.12 |
頁 次 | 頁139-148 |
分類號 | 493.1 |
關鍵詞 | 常態分配; 數值微分; 捨位誤差; 截斷誤差; 選擇權; 定價公式; Normal distribution; Numerical differentiation; Round off error; Truncation error; Option; Pricing formula; |
語 文 | 中文(Chinese) |
中文摘要 | 現在選擇權的種類越來越多,各種各樣的定價公式也非常複雜甚至無法求解。因而常必須以數值方法替代解析解,但是在數值計算的過程中,很容易引入額外的計算誤差,包括捨位誤差典截斷誤差。不當套用將對計算結果產生很大的影響。本文的目的即在探討,因不當使用數值計算而產生的誤差有多大,文中並以常態分配之數值微分為例。結果顯示,採用適當的數值計算方法,不僅可以降低計算量,更能夠大幅度降低誤差,根據實際計算例的結果,可降低 444 倍。 |
英文摘要 | There are many types of option. The relevant pricing formulas are very complex and hard to solve. Hence, we often use numerical methods to calculate the price of options. But in the numerical calculation process, such as numerical differentiation, if we use these numerical methods inadequately, then it may be induced non necessary numerical error, including round off and truncation error. The purpose of this paper is to investigate the error magnitude caused by improper using of numerical calculation only. The numerical differentiation of Normal Probability Distribution is examined as an example. The results show that proper use of numerical calculation procedure can reduce numerical error dramatically. According to the case we studied, the error can be reduced to 444 times. |
本系統中英文摘要資訊取自各篇刊載內容。