臺灣博碩士論文加值系統

自從Black-Scholes在1973年提出選擇權定價模型後，就有許多相關選擇權定價的理論及實證的研究出現。而Black-Scholes的選擇權定價只適用於歐式選擇權的定價，但在市場上所交易的大多是美式選擇權。故本篇論文將利用美式選擇權模型訂價以減少其定價誤差。所使用的資料是來自於芝加哥商業交易所（CME）的外匯期貨選擇權，並運用不同的美式外匯期貨選擇權定價模型來做定價。此外，也探討在不同定價模型下，成交量、價內程度、選擇權到期日及標的資產報酬與定價誤差之間的關係。希望此結果能帶給企業、個人及投資者些許參考價值。
此篇將實證研究分為兩部分：
第一部份，我們使用不同美式外匯期貨選擇權定價模型來進行定價。這些模型包括（1）Barone-Adesi and Whaley（1987）的二次估計法（Quadratic Approximation Method）；（2）Geske and Johnson（1984）的Richardson外差法（Richardson Extrapolation Method）；（3）Tsai, Shyu, and Liao（1999）的隱含相信值（Implied Belief Value）；（4）蒙地卡羅模擬法（Monte Carol Simulation）。這些模型原本使用於股票選擇權市場，現在我們將這些模型修正成適用於美式外匯期貨選擇權的定價模型。且利用這些修正後的模型來進行定價，並與市場價格相比較其誤差情形。
在外匯期貨選擇權的定價模型中，除了外匯期貨的波動性之外，所有的變數均可以從市場資料中取得。我們使用兩種不同的波動性估計方法，來計算其外匯期匯的波動性，並將其值代入不同的美式外匯期貨選擇權定價模型之中。
第二部分，此篇文章將使用迴歸分析探討不同定價模型下，成交量、價內程度、選擇權到期日及標的資產報酬與定價誤差之間的關係。最後，本篇文章所得到的實證結果顯示：
1.研究發現外匯期貨選擇權市場無效率，且無法明確指出在不同模型下何者的定價誤差較小。
2.研究發現在外匯期貨選擇權市場裡，成交量大會造成定價誤差減少或增加的情形。
3.美式外匯期貨選擇權定價模型會有低估價外選擇權及高估價內選擇權的情形。
4.選擇權定價誤差與選擇權離到期日有反向關係，即離到期日愈遠則定價誤差愈小，離到期日愈近則定價誤差愈大。
5.選擇權定價誤差與標的資產報酬有正向關係，即標的資產報酬愈高則定價誤差愈大，標的資產報酬愈低則定價誤差愈小。

Since Black and Scholes published their option pricing model in 1973, there has been numerous of theoretical and empirical work of option pricing. Black and Scholes’s option pricing formula was just for the evaluation of European-type options, most traded options were American-type options. However, this paper uses American option pricing formula for the evaluation of American options to reduce the mispricing of the American-type options. We use the data of foreign currency futures options from the Chicago Mercantile Exchange（CME）to compare their forecasting performance of various of American option pricing models.
Besides, we examine the relation between volume, In-, At-, and Out-of-the-Money-Classes, the time to maturity of the options, and the degree of underlying asset price return and mispricing in the option pricing model. The result provides some reference value for the enterprises, individuals, and investors.
This study divides the empirical research into two parts：
In the first part, we use some American currency futures option pricing models proposed by（1）the Barone-Adesi and Whaley（1987）’s Quadratic Approximation Method；（2）the Geske and Johnson（1984）’s Richardson Extrapolation Method；（3）Tsai, Shyu, and Liao（1999）’s Implied Belief Value；（4）Monte Carol Simulation. The models originally were used in stock option market and now we make some corrections in these models. After correcting these option pricing model, we use these models to compute the theory price and compare it with the market price and if there exits obvious difference.
In foreign currency futures option pricing model, all the other variables can be obtained from the market data except the currency futures volatility. The option price is computed using two different methods of computing the unobservable volatility input. Specifically, we compute the currency futures volatility by using History Volatility Approach and GARCH model and substitute it into the American currency futures option pricing model.
In the second part, this paper uses the Regression Analysis Tests to examine the volume effect on option mispricing within the options market. In addition, we also examine the other factor which affect the pricing error, include In-, At-, and Out-of-the-Money Classes, the time to maturity of the options, and the degree of underlying asset return. Finally, this paper gets some result as follow：
(1) The findings indicate inefficiency in these option markets and/or inaccuracy in the specification of the model.
(2) The results indicate that dual relation between mispricing in these American currency futures option pricing models and volume in the JY futures option market.
(3) The model undervalues out-of-the-money options and overvalues in-the-money options.
(4) The degree of relative mispricing of options is decreasing function of the time to maturity of options.
(5) The degree of relative mispricing of options is increasing function of the degree of underlying asset price return.

Table of Contents
Page
論文摘要…………………………………………………………….....Ⅰ
Abstract………………………………………………………………….Ⅲ
Index of Tables and Figures………………………………………..Ⅶ
Table of Symbols………………………….………………………… .Ⅸ
Chapter One：Introduction…………………………………………...1
1.1 Background of Study...…………………………………...1
1.2 Purpose of Study…………………………………………….5
1.3 Procedures of Study…………………………………………9
1.4 Framework of Study…………………………………………10
Chapter Two：Literature Review…………………………………….13
2.1 Currency and Currency Futures Options Overview…….13
2.1.1 Currency Options Overview………………………….13
2.1.2 Currency Futures Option Overview…………………15
2.1.3 Currency Option Pricing Models and Empirical
Research......................................18
2.1.4 Some Empirical Researches on Options Pricing
Formulas………….….……......................22
2.1.5 Futures Option Pricing Models and Empirical
Researches…….……….……....................26
2.2 American Option Pricing Models………………………….31
2.3 The Research of Option Pricing Error………………….37
2.3.1 The Relationship between the Pricing Error and
Standard Deviations....……...................38
2.3.2 The Relationship between the Pricing Error and
Volume……………………........................39
Chapter Three：Methodology………………………………………….44
3.1 The American Currency Futures Option Model………….44
3.2 The Methods for Volatility Estimation…………………50
3.2.1 Measurement of Historical Volatility Model……51
3.2.2 Generalized Autoregressive Conditional
Heteroscedasticity（GARCH）Model..............52
3.3 Comparing the Forecasting Performance of the Models53
3.3.1 Evaluation of Forecasting Performance………….53
3.3.2 Measuring of Mispricing and Standard Deviations.53
3.3.3 Regression Analysis Tests………………………….54
Chapter Four：Data Collection and Empirical Results…………57
4.1 Data Collection………………………………………………57
4.2 Data Description…………………………………………….58
4.2.1 Currency Futures………………………………………58
4.2.2 Currency Futures Options……………………………58
4.3 Empirical Results……………………………………………60
4.3.1 The Average Prices and Standard Deviations……60
4.3.2 The Forecasting Performance of the Models…….64
4.3.3 Regression Tests for Biases in the Pricing
Models…......................................72
Chapter Five：Conclusions and Suggestions………………………85
5.1 Conclusions for the Study…………………………………85
5.2 Suggestions for Further Study……………………………87
Appendix……………………………………………………………..….89
References..…………………………………………………………...93
Index of Tables and Figures
Figure 1-1 Procedures of Study……………………………………..9
Table 2.1 PHILADELPHIA BOARD OF TRADE
CURRENCY OPTIONS CONTRACT SPECIFICATION……………14
Table 2.2 CME BOARD OF TRADE
CURRENCY FUTURES CONTRACT SPECIFICATIONS………….16
Table 2.3 The Main Differences between Currency Options and
Currency Futures Options……………………………….18
Table 2.4 Some Empirical Researches on Black-Scholes Options
Formulas………...................................23
Table 2.5 Some Empirical Researches on the Basis of Other
Pricing Models…….…............................25
Table 2.6 There are Some Related Literatures of the Futures
Option...……………..............................30
Table 4.1 Data Source…………………………………………………58
Table 4.2 Currency Futures Data Description……………………58
Table 4.3 Currency Futures Options Data Description…………59
Table 4.4 The Theoretical Average Value under Historical
Volatility Model………...........................61
Table 4.5 The Theoretical Average Value under GARCH (1,1)
Model….……...…................................63
Table 4.6 Comparisons of Alternative Model Forecasts
Historical Volatility （October）……………………66
Table 4.7 Comparisons of Alternative Model Forecasts.
Historical Volatility （November）………………….67
Table 4.8 Comparisons of Alternative Model Forecasts.
Historical Volatility （December）………………….68
Table 4.9 Comparisons of Alternative Model Forecasts.
GARCH (1,1) Model （October）…………………………69
Table 4.10 Comparisons of Alternative Model Forecasts.
GARCH (1,1) Model （November）……………………….70
Table 4.11 Comparisons of Alternative Model Forecasts.
GARCH (1,1) Model （December）………………………71
Table 4.12 Factors Affecting the Performance of the Black-
Scholes Option Pricing Models in the Historical
Volatility Model………..……………..……..…....75
Table 4.13 Factors Affecting the Performance of the Black-
Scholes Option Pricing Models in the GARCH （1,1）
Model………………………….…..……..............76
Table 4.14 Factors Affecting the Performance of the Quadratic
Approximation Option Pricing Models in the
Historical Volatility Model……….……..………..77
Table 4.15 Factors Affecting the Performance of the Quadratic
Approximation Option Pricing Models in the GARCH
（1,1）Model……………………...…..…............78
Table 4.16 Factors Affecting the Performance of the Richardson
Extrapolation Option Pricing Models in the
Historical Volatility Model……..……..………….79
Table 4.17 Factors Affecting the Performance of the Richardson
Extrapolation Option Pricing Models in the GARCH
（1,1） Model…………………...……….............80
Table 4.18 Factors Affecting the Performance of the Simulation
Option Pricing Models in the Historical Volatility
Model……………………..……..….................81
Table 4.19 Factors Affecting the Performance of the Simulation
Option Pricing Models in the GARCH （1,1） Model82
Table 4.20 Factors Affecting the Performance of the Implied
Belief Value Option Pricing Models in the Historical
Volatility Model………………………..............83
Table 4.21 Factors Affecting the Performance of the Implied
Belief Value Option Pricing Models in the GARCH
（1,1） Model……………………...…….............84
Table 5.1 The results of Regression Tests………………………86

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柯讚恩（1997），「美式期貨選擇權評價模式之實證研究」，中興大學經濟研究所碩士論文。
徐守德，官顯庭，黃玉娟（1998），「台股認購權證定價之研究」，管理評論，第十七卷，第二期，民國八十七年七月，pp.45-69。
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蔡明憲（1999），「有試用期選擇權及美式選擇權的定價與應用」，中山大學財管所博士論文。
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