THE BLACK SCHOLES FORMULA
THE BLACK SCHOLES FORMULA
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布莱克·斯科尔斯公式
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
Myron S. Scholes
中科院分区：
文献类型：
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作者：
Mark H.A. Davis;Myron S. Scholes
“如果在市场上正确定价，则不可能通过使用此原则在期权中创建长位置和较短的职位来确保利润Fischer Black和Myron Scholes在选项定价上的摘要[2]的前两个句子，并封装了基本思想，也就是说 - 与他们的资产价格模型一样员工 - 缺乏套利足以获得该资产的呼叫选项的独特价值，（1.4）是金融经济学中最著名的公式，实际上，整个主题是果断的黑色前舞和黑色后时代。基于风格化的数学模型，该模型并不是对实际资产价格的特别准确的代表，但事实证明，在期权交易的世界中，这是如此有效。公式同样可以以部分差分方程（PDE）的形式说明。选项“希腊人”，而第4节则介绍了实际上是一种更有用的黑色 - 智能形式，通常称为“黑色公式”。波动性并证明了黑色choles的“鲁棒性”特性，这意味着即使“真实的”价格过程与黑人和Scholes有根本不同，也可以实现有效的对冲程式化模型。
‘If options are correctly priced in the market, it should not be possible to make sure profits by creating portfolios of long and short positions in options and their underlying stocks. Using this principle, a theoretical valuation formula for options is derived.’ These are the first two sentences of the abstract of the great paper [2] by Fischer Black and Myron Scholes on option pricing, and encapsulate the basic idea, which is that—with the asset price model they employ—insisting on absence of arbitrage is enough to obtain a unique value for a call option on that asset. The resulting formula, (1.4) below, is the most famous formula in financial economics, and in fact that whole subject splits decisively into the pre-Black-Scholes and post-Black-Scholes eras. This article aims to give a self-contained derivation of the formula, some discussion of the hedge parameters, and some extensions of the formula, and to indicate why a formula based on a stylized mathematical model which is known not to be a particularly accurate representation of real asset prices has nevertheless proved so effective in the world of option trading. Section 1 formulates the model and states and proves the formula. As is well known, the formula can equally well be stated in the form of a partial differential equation (PDE); this is equation (1.5) below. Section 2 discusses the PDE aspects of Black-Scholes. Section 3 summarizes information about the option ‘Greeks’, while Sections 4 and 5 introduce what is actually a more useful form of Black-Scholes, usually known as the ‘Black formula’. Finally, Section 6 discusses the applications of the formula in market trading. We define the implied volatility and demonstrate a ‘robustness’ property of Black-Scholes which implies that effective hedging can be achieved even if the ‘true’ price process is substantially different from Black and Scholes’ stylized model.