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論文名稱 Title |
平均選擇權數值訂價方法之比較 A Comparsion of Numerical Pricing Mthods for Average Options |
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系所名稱 Department |
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畢業學年期 Year, semester |
語文別 Language |
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學位類別 Degree |
頁數 Number of pages |
57 |
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研究生 Author |
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指導教授 Advisor |
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召集委員 Convenor |
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口試委員 Advisory Committee |
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口試日期 Date of Exam |
2003-06-09 |
繳交日期 Date of Submission |
2003-08-29 |
關鍵字 Keywords |
平均選擇權、亞式選擇權、數值方法 Numerical Methods, Average Options, Asian Options |
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統計 Statistics |
本論文已被瀏覽 5729 次,被下載 35 次 The thesis/dissertation has been browsed 5729 times, has been downloaded 35 times. |
中文摘要 |
本研究針對平均式選擇權(亦稱亞式選擇權)在市場上最廣泛的 產品類型—歐式、離散型、算數平均式選擇權—比較其各種數值評價 方法之訂價精確度。 傳統上,財務領域通常假定資產的動態行為服從幾何布朗運動, 但在此假定下,平均式選擇權之訂價並沒有解析封閉解存在。故自 1990 年以來,陸續有許多數值評價方法被提出來。這些數值評價方 法大致可以分為下列六類:1.蒙地卡羅法(含變異數降低技術與半蒙 地卡羅法);2.修正之樹形法或格子法;3.偏微分方程法;4.一般數值 法;5.假解析特徵法;與6.解析近似法等。在過去的文獻中多是針對 個別評價方法類型進行比較(且以一般Crude 蒙地卡羅法作為評價 之標竿),鮮少針對不同方法之訂價精準度進行比較,故本文以此為 題進行研究。 由於平均式選擇權之變化種類並不少,故本研究以市場上最廣泛 發行之類型—歐式、離散型、平均式選擇權—為主要標的,比較其三 種常見的評價方法在訂價上之相對精確度,此三類評價方法分別為: 1.蒙地卡羅法;2.修正之樹形法或格子法;3.解析近似法。 本文之研究結論為,對於歐式離散型平均式選擇權而言,蒙地卡 羅法中之控制變異法之訂價精準度最高外,在計算速度與實作彈性上 均很高,故該法為此類商品訂價過程中最適之評價方法。 |
Abstract |
In this thesis, we survey some popular pricing methods of average options. They can be classified into three cateogries include approximation, Monte Carlo, and binomial tree approaches. We examine the accuracy of these methods by two cases, exchange rate and stock price. Numerical testing results show the accuracy of approximation and binomial tree are not stable. For the big-size feature of average option, their outputs are doubtful and damaging in pactice. Despite this, they are still valuable. This is because they own the other advantages. For example, the approximation approach can give us a quick formlas to calculate the Greek, and the binomial tree approach can price the American style options. |
目次 Table of Contents |
1. Introduction……………………………………………………… 1 1.1 Background………...…………………………………………….1 1.2 Ontline………………...……………………………………….1 2. Review of Options Theories…………………………………… 3 2.1 Basic Assumption in Finance ……………………………….3 2.2 Underlying Processes…………….....……………………………4 2.3 Ito’s Lemma……………………..…………………………….5 2.4 Risk Neutral Valuation………………………………………...7 3. Average Options……………………………………………… 16 3.1 Average Options……………………………………………...16 3.2 Literatures Review………………………………………......19 4. Pricing Average Options……………………………………… 21 4.1 The Model and Notation Setting…………………………......21 4.2 Pricing Methods of Average Options……………………......23 5. Numerical Testing……………………………………………… 43 5.1 Numerical Testing 1 (Exchange Rate) ……………..……......43 5.2 Numerical Testing 1 (Exchange Rate) ……………..……......52 6. Conclusion……………………………………………………... 61 Bibliography……………………………………………………... 62 |
參考文獻 References |
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