探討布萊克-休斯徧微分方程之解

study on option pricing model－ Black-Scholes partial differential equation

黃鼎銘(Ting-Ming Huang)

指導教授 ： 林賜德

中原大學/理學院/數學研究所/碩士(2002年)

https://doi.org/10.6840/cycu200200225

摘要

摘 要

在1973年Fisher. Black和Myron Scholes [3]利用熱能替換公式，而推演出的選擇權評價公式，這個公式給予財務領域的理論學者莫大的影響，從此許多新的研究都奠基於此一公式，如Bensoussan, A. Crouhy M. and Galai D.[2]， Hull, J. C and white A [5]等等…。本研究主要是針對純粹選擇權（或標準化的選擇權）加以探討。首先，回顧Fisher. Black和Myron Scholes [3]並說明Wyss[6]。最後嘗試以柯西-尤拉定理求微分方程解的原理和利用Nishimoto[7]的方法，去找到選擇權的評價解。

關鍵字

選擇權

並列摘要

Abstract

In 1973, Fisher. Black and Myron. Scholes [3] solved the Options valued formula with the Heart Exchange Equations. Theoretical professionals in financial field were affected deeply by the formula. And many new researches have been based by it, like Bensoussan, A. Crouhy M. and Galai D.[2], Hull, J. C and white A [5]…….
The paper remains to study the Plain Vanilla Options（or standardized Options）. First, I review Fisher. Black and Myron. Scholes [3] and explain Wyss [6]. Finally, I try to solve the differential equation by using Cauchy-Euler Theorem and Nishimoto Lemma.

並列關鍵字

option

參考文獻

[1]A. Erde’lyi et al. (Ed-s), Tables of Integral Transforms,

equity volatility related to the leverage effect ：valuation

[3]Black, F., and Scholes, M. 1973 “ The Pricing and Corporate Liabilities ”. Journal of Political Economy 81：637-654.

[4]Fox, Ch. The G and H functions as symmetrical Fourier Kernels. Trans. Amer. Math. Soc. 98(1961), 395-429.

[5]Hull, J. C. and White, A. (1987) The pricing of options on assets with stochastic volatilities, J. Finance, 42, 281-300.