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研究生:莊千卉
研究生(外文):Chuang Chienhui
論文名稱:選擇權市場上的震盪作用-傅利葉展開
論文名稱(外文):An Oscillatory affection on the Option Market - The Fourier Expansion
指導教授:傅學舜
學位類別:碩士
校院名稱:輔仁大學
系所名稱:數學系研究所
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:2007
畢業學年度:95
語文別:中文
論文頁數:38
中文關鍵詞:選擇權
外文關鍵詞:OPTIONS
相關次數:
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在 1973 年 Fisher Black 和 Myron Scholes
利用熱能替換公式推導出選擇權評價公式的解。
但是它只用在完美市場的情況下。所以我們利用 Fourier
series的概念,給此原方程一個有固定震盪頻率的外力,
以 sine 級數來表示在某個時間點有人想抬高股票價格,
但又在某些時間點有另外的一批人想壓低股價,導致市場上股價一直有上下波動的情況發生。
最後再探討我們有外力的選擇權價格的解和 Black-Scholes
原方程的解之間的不同。
In 1973, Fisher Black and Myron Scholes solved the options valued
formula with the Heat Exchange Equations. But it is used in a perfect market.
We use the concept of Fourier series to express an oscillation by outer force
for the original equation. Using the sine series, it represents that some person
wants to raise the stock price in some time, but some other people want to reduce
the stock price in certain time. Therefore the stock price undulation always
occurs in the market. Finally, we discuss the difference of the solutions
of the option price with outer force and the Black-Scholes original
equation.
1. Introduction
2. Fundations and Results
2.1 Heat Equation
2.2 The Schwartz Space
2.3 The Fourier Series
2.4 The Fourier Transform
2.5 Tempered Distributions
2.6 The Homogenous and Non-homogenous Black-Scholes Model
2.7 The Convergence of solutions in the space of distribution
[1] G. Barles and H. M. Soner, Option pricing with transaction
costs and a nonlinear Black-Scholes equation, Finance Stochast. 2 (1998)
369-397.
[2]F. Black and M. Scholes, The price of options and
corporate liabilites, Journal of Political Economy ,81 (1973),637-659.
[3] P. Boyle and T. Vorst, Option replication in discrete time
with transaction costs, J. Finance. 47 (1992) 271-293.
[4] M. Davis, V. Panis and T. Zariphopoulou, European option
pricing with transaction fees, SIAM J. Contr. Optim. 31 (1993) 470-493.
[5] J. Dewynne, S. Howison and P. Wilmott, Option Pricing:
Mathematical Models and Computation (Oxford, Financial Press, 1995).
[6] R. Frey, Perfect option hedging for a large trader,
Finance Stochast. 2 (1998) 115-141.
[7] R. Frey, Market illiquidity as a source of model risk in
dynamic hedging, in Model Risk, R. Gibson, ed. (RISK Publications, London,
2000).
[8] G. Genotte and H. Leland, Market liquidity, hedging and
crashes, Amer. Econ. Rev. 80 (1990) 999-1021.
[9] R. Jarrow, Market manipulation, bubbles,corners and short
squeezes, j. Financial Quant. Anal. 27 (1992) 311-336.
[10] J. Leitner, Continuous time CAPM, price for risk and
utility maximization, in Mathematical Finance, M. Kohlmann et al.ed.
Workshop of the Mathematical Finance Research Project, Konstanz, Germany
(Birkh\"{a}user, Basel, 2001).
[11]R. C. Merton, Theory of rational option pricing, Bell J.
Econ. Manag. Sci. 4 (1973) 141-183.
[12]E. Platen and M. Schweizer, On feedback effects from
hedging derivatives, Math. Finance. 8 (1998) 67-84.
[13]P. Sch\"{o}nbucher and P. Wilmott, The feedback effect of
hedging in illiquid mackets, SIAM J. Appl. Math. 61 (2000) 232-272.
[14] John Hull, Options, Futures, and other Derivatives,
ch11$\sim$ ch12.
[15]Jeffrey Rauch, Partial Differential Equations, ch2$\sim$
ch3.
[16] Stanley J. Farlow, Partial Differential Equations for Scientists and Engineers.
[17]陳宏,郭震坤, 財務數學(上),數學傳播季刊,第26卷第1期,中央研究院數學研究所發行.
[18]陳宏,郭震坤, 財務數學(下),數學傳播季刊,第26卷第2期,中央研究院數學研究所發行.
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