摘要翻译：
本文研究了连续时间市场模型中的股票期权定价问题，模型中存在两个随机可交易资产，其中一个被选为非随机资产。研究表明，在Num\eraire过程的演化过程中，任意小的随机偏差的存在会引起市场性质的显著变化。特别地，一个等价鞅测度对这个市场不是唯一的，并且存在不可复制的主张。对于等价鞅测度的某些极端选择，鞅价格和套期保值误差可以显著变化并取极值。提出并讨论了等价鞅测度的一些合理选择，包括由观察到的债券价格计算出的隐含测度。这允许计算风险过程的隐含市场价格。
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英文标题：
《On martingale measures and pricing for continuous bond-stock market with
  stochastic bond》
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作者：
Nikolai Dokuchaev
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最新提交年份：
2014
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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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一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Quantitative Finance        数量金融学
二级分类：Computational Finance        计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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英文摘要：
  This papers addresses the stock option pricing problem in a continuous time market model where there are two stochastic tradable assets, and one of them is selected as a num\'eraire. It is shown that the presence of arbitrarily small stochastic deviations in the evolution of the num\'eraire process causes significant changes in the market properties. In particular, an equivalent martingale measure is not unique for this market, and there are non-replicable claims. The martingale prices and the hedging error can vary significantly and take extreme values, for some extreme choices of the equivalent martingale measures. Some rational choices of the equivalent martingale measures are suggested and discussed, including implied measures calculated from observed bond prices. This allows to calculate the implied market price of risk process.
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PDF链接：
https://arxiv.org/pdf/1108.0719