英文标题：
《Information in stock prices and some consequences: A model-free approach》
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作者：
Yannis G. Yatracos
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最新提交年份：
2015
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英文摘要：
The price of a stock will rarely follow the assumed model and a curious investor or a Regulatory Authority may wish to obtain a probability model the prices support. A risk neutral probability ${\\cal P}^*$ for the stock\'s price at time $T$ is determined in closed form from the prices before $T$ without assuming a price model. The findings indicate that ${\\cal P}^*$ may be a mixture. Under mild conditions on the prices the necessary and sufficient condition to obtain ${\\cal P}^*$ is the coincidence at $T$ of the stock price ranges assumed by the stock\'s trader and buyer. This result clarifies the relation between market\'s informational efficiency and the arbitrage-free option pricing methodology. It also shows that in an incomplete market there are risk neutral probabilities not supported by each stock and their use can be limited. ${\\cal P}^*$-price $C$ for the stock\'s European call option expiring at $T$ is obtained. Among other results it is shown for \"calm\" prices, like the log-normal, that i) $C$ is the Black-Scholes-Merton price thus confirming its validity for various stock prices, ii) the buyer\'s price carries an exponentially increasing volatility premium and its difference with $C$ provides a measure of the market risk premium.
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中文摘要：
股票价格很少遵循假设模型，好奇的投资者或监管机构可能希望获得价格支持的概率模型。在不假设价格模型的情况下，从$T$之前的价格以封闭形式确定$T$时股票价格的风险中性概率${\\cal P}^*$。研究结果表明${\\cal P}^*$可能是一种混合物。在价格温和的条件下，获得${\\cal P}^*$的充分必要条件是，股票交易人和买方假定的股票价格区间在$T$处重合。这一结果澄清了市场信息效率与无套利期权定价方法之间的关系。它还表明，在一个不完备的市场中，存在每只股票都不支持的风险中性概率，它们的使用可能是有限的${\\cal P}^*$-获得到期日为$T$的股票欧洲看涨期权的价格$C$。在其他结果中，对于“平静”价格，如对数正态分布，表明i）$C$是Black Scholes-Merton价格，从而确认其对各种股票价格的有效性；ii）买方价格具有指数级增加的波动性溢价，其与$C$的差异提供了市场风险溢价的度量。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：General Finance 一般财务
分类描述：Development of general quantitative methodologies with applications in finance
通用定量方法的发展及其在金融中的应用
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一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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