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摘要翻译：
利用Dirichlet形式理论的方法，研究了参数不确定性对随机扩散模型的影响，特别是对未定权益定价的影响。我们将这些技术应用于套期保值过程，以计算SDE轨迹对参数扰动的敏感性。我们证明了这种分析可以内生性地证明期权价格上存在买卖价差。我们还证明了如果随机微分方程具有闭式表示，则灵敏度也有闭式表示。我们检验了对数正态扩散的情形，我们证明了这个框架导致了一个微笑的隐含波动率面与历史数据相一致。
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英文标题：
《Asset Pricing under uncertainty》
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作者：
Simone Scotti (LPMA)
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最新提交年份：
2012
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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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英文摘要：
We study the effect of parameter uncertainty on a stochastic diffusion model, in particular the impact on the pricing of contingent claims, using methods from the theory of Dirichlet forms. We apply these techniques to hedging procedures in order to compute the sensitivity of SDE trajectories with respect to parameter perturbations. We show that this analysis can justify endogenously the presence of a bid-ask spread on the option prices. We also prove that if the stochastic differential equation admits a closed form representation then the sensitivities have closed form representations. We examine the case of log-normal diffusion and we show that this framework leads to a smiled implied volatility surface coherent with historical data.
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PDF链接：
https://arxiv.org/pdf/1203.5664
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