英文标题：
《Small-time expansions for state-dependent local jump-diffusion models
with infinite jump activity》
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作者：
Jos\\\'e E. Figueroa-L\\\'opez and Yankeng Luo
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最新提交年份：
2015
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英文摘要：
In this article, we consider a Markov process X, starting from x and solving a stochastic differential equation, which is driven by a Brownian motion and an independent pure jump component exhibiting state-dependent jump intensity and infinite jump activity. A second order expansion is derived for the tail probability P[X(t)>x+y] in small time t, for y>0. As an application of this expansion and a suitable change of the underlying probability measure, a second order expansion, near expiration, for out-of-the-money European call option prices is obtained when the underlying stock price is modeled as the exponential of the jump-diffusion process X under the risk-neutral probability measure.
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中文摘要：
在这篇文章中，我们考虑一个马尔可夫过程X，从X开始，求解一个随机微分方程，它由一个布朗运动和一个独立的纯跳跃分量驱动，表现出与状态相关的跳跃强度和无限的跳跃活动。在小时间t内，当y>0时，导出了尾概率P[X（t）>X+y]的二阶展开式。作为该展开式的应用和基础概率测度的适当变化，当基础股票价格在风险中性概率测度下被建模为跳跃扩散过程X的指数时，得到了货币外欧洲看涨期权价格在到期时的二阶展开式。
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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
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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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