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研究生:顏琦華
研究生(外文):Chi-Hua Yen
論文名稱:擾動法求解考慮流動性Black-Scholes選擇權評價模型
論文名稱(外文):Perturbation Method in Liquidity-Adjusted Black-Scholes Equation
指導教授:賴振耀賴振耀引用關係
學位類別:碩士
校院名稱:國立中正大學
系所名稱:應用數學研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2001
畢業學年度:89
語文別:中文
論文頁數:36
中文關鍵詞:擾動流動性數值偏微分方程
外文關鍵詞:PerturbationLiquiditynumerical PDE
相關次數:
  • 被引用被引用:1
  • 點閱點閱:389
  • 評分評分:
  • 下載下載:0
  • 收藏至我的研究室書目清單書目收藏:0
  隨著衍生性商品在非流動性市場的交易量增加,當評價其價值時,必須將市場的流動性納入考量。Krakovsky(1999)將市場的流動性納入Black-Scholes(1973)的分析中,並推導出考慮流動性之Black-Scholes選擇權評價模型,此為一非線性的偏微分方程式,對於簡單的歐式選擇權也難以求出其封閉解,故本文嘗試使用擾動法將此非線性的偏微分方程式重新整理,並利用有限差分法之理論來分析所求得之數值解。

Pricing market liquidity into derivatives has become essential as the use of equity and fixed-income derivatives in illiquid markets has increased. However, the Liquidity-adjusted Black-Scholes equation is non-linear and cannot be solved in a closed form even for simple European-style options due to the complexity of the gamma term. In the paper, we try to apply perturbation method in the Liquidity-adjusted Black-Scholes equation, and then use finite difference methods to solve the
partial differential equation numerically.

1. INTRODUCTION ........ 4
2. LIQUIDITY - ADJUSTED BLACK - SCHOLES EQUATION ........ 5
3. METHODOLOGY 8
3.1 Perturbation Method ........ 8
3.2 The initial and Boundary Conditions ........ 11
3.3 Logarithmic Transform ........ 13
3.4 The Weighted Average Method ........ 14
3.5 Algorithm ........ 17
4. NUMERICAL RESULT 21
4.1 Call Option price, Delta, and Gamma ........ 21
4.2 Put-Call Parity ........ 24

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[13]蘇敏娟, "考慮流動性之選擇權評價模型:顯性有限差分法之探討",
國立中正大學應用數學研究所, 民國89年.
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國立中正大學應用數學研究所, 民國89年.
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"Moving Mesh and Grid Adaption : Survey and Application",
國立中正大學應用數學研究所, 民國88年.
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五南圖書出版公司, 民國87年.

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