臺灣博碩士論文加值系統

隨著選擇權在台灣期貨交易所的成交量日漸增加，如何正確且快速的定價選擇權也日漸重要。Black 及 Sholes (1973) 提供了一個相當有用的定價模型，但卻有太多不合理的限制。本篇論文使用了Duan、Ritchen 及Sun (2006)的定價模型，其模型包含了GARCH 及跳躍過程。藉由Silva 及Barbe (2005)提供的方式，我們使用調整後的準蒙地卡羅模擬去改善模擬的效率以得到正確的選擇權價格。

With the trade volume increasing in TAIEX option, how to price the options correctly and quickly becoming more and more important. Black and Sholes (1973)
provided a useful model to price the options; however, it has many estrictions. In the paper, we introduce the option pricing model developed by Duan, Ritchen and Sun (2006) which both GARCH and jump processes are included. By applying the
quasi-Monte Carlo simulation method adjusted by Silva and Barbe (2005), we improve the efficiency of simulation.

CHAPTER 1 INTRODUCTION................................................................................1
CHAPTER 2 LITERATURE REVIEW ....................................................................3
2.1. OPTION PRICING MODELS...............................................................................3
2.2. THE MONTE CARLO SIMULATION....................................................................6
2.3. WAYS TO IMPROVE THE EFFICIENCY OF THE MONTE CARLO SIMULATION........8
CHAPTER 3 METHODLOGY..................................................................................9
3.1. APPROXIMATING THE GARCH-JUMP OPTION PRICING MODEL........................9
3.2. GENERATION OF THE LOW-DISCREPANCY SEQUENCE OF SOBOL.....................15
CHAPTER 4 NUMERICAL RESULT ....................................................................18
4.1. APPLY THE QUASI-MONTE CARLO METHOD TO THE B-S MODEL ...................18
4.2. APPLICATION OF SOBOL SEQUENCE TO APPROXIMATING GARCH-JUMP
MODELS........................................................................................................24
CHAPTER 5 CONCLUSIONS.................................................................................37
APPENDIX.................................................................................................................38
1. THE GARCH OPTION PRICING MODELS ............................................................38
2. SOBOL’S NUMBERS (K=1)..................................................................................40
I

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