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摘要翻译：
在本文中，我们构造了一个给定的离散时间网格中，股票价格过程具有与几何布朗运动相同的边缘对数正态律，并且在任意两个时刻之间具有相同的转移密度（和收益分布）。然后，我们说明了基于这种过程的期权价格与Black和Scholes的期权价格的不同之处，因为期权价格可以任意接近于期权内在价值，也可以任意接近于标的股票价格。我们还解释了这是由于在与交易相关的网格时间瞬间之间建模股票价格过程的特殊方式。本文详细介绍了具有规定扩散系数且密度以规定指数族演化的标量随机微分方程的理论结果。
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英文标题：
《Discrete Time vs Continuous Time Stock-price Dynamics and implications
for Option Pricing》
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作者：
Damiano Brigo and Fabio Mercurio
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最新提交年份：
2008
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Pricing of Securities 证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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英文摘要：
In the present paper we construct stock price processes with the same marginal log-normal law as that of a geometric Brownian motion and also with the same transition density (and returns' distributions) between any two instants in a given discrete-time grid. We then illustrate how option prices based on such processes differ from Black and Scholes', in that option prices can be either arbitrarily close to the option intrinsic value or arbitrarily close to the underlying stock price. We also explain that this is due to the particular way one models the stock-price process in between the grid time instants which are relevant for trading. The theoretical result concerning scalar stochastic differential equations with prescribed diffusion coefficient whose densities evolve in a prescribed exponential family, on which part of the paper is based, is presented in detail.
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PDF链接：
https://arxiv.org/pdf/0812.4010
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