摘要翻译:
再次讨论了亚椭圆扩散$(x^1,...,x^d)$的密度展开式。特别是,我们对投影$(x_t^1,...,x_t^l)$的密度展开感兴趣,在$t>0$时,使用$l\leq d$。找到了取代热核渐近中已知的“不在切点内”条件的全局条件。我们的小噪声扩展允许一个“二阶”指数因子。作为应用,布朗运动的Takanobu-Watanabe展开式和Levy随机区域得到了新的启示。进一步的应用包括一些随机波动率模型中的尾部和隐含波动率渐近,在一篇论文中讨论了这一点。
---
英文标题:
《Marginal density expansions for diffusions and stochastic volatility,
part I: Theoretical Foundations》
---
作者:
J. D. Deuschel, P. K. Friz, A. Jacquier, S. Violante
---
最新提交年份:
2013
---
分类信息:
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
--
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
--
---
英文摘要:
Density expansions for hypoelliptic diffusions $(X^1,...,X^d)$ are revisited. In particular, we are interested in density expansions of the projection $(X_T^1,...,X_T^l)$, at time $T>0$, with $l \leq d$. Global conditions are found which replace the well-known "not-in-cutlocus" condition known from heat-kernel asymptotics. Our small noise expansion allows for a "second order" exponential factor. As application, new light is shed on the Takanobu--Watanabe expansion of Brownian motion and Levy's stochastic area. Further applications include tail and implied volatility asymptotics in some stochastic volatility models, discussed in a compagnion paper.
---
PDF链接:
https://arxiv.org/pdf/1111.2462