英文标题：
《Probability density of lognormal fractional SABR model》
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作者：
Jiro Akahori, Xiaoming Song, and Tai-Ho Wang
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最新提交年份：
2019
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英文摘要：
Instantaneous volatility of logarithmic return in the lognormal fractional SABR model is driven by the exponentiation of a correlated fractional Brownian motion. Due to the mixed nature of driving Brownian and fractional Brownian motions, probability density for such a model is less studied in the literature. We show in this paper a bridge representation for the joint density of the lognormal fractional SABR model in a Fourier space. Evaluating the bridge representation along a properly chosen deterministic path yields a small time asymptotic expansion to the leading order for the probability density of the fractional SABR model. A direct generalization of the representation to joint density at multiple times leads to a heuristic derivation of the large deviations principle for the joint density in small time. Approximation of implied volatility is readily obtained by applying the Laplace asymptotic formula to the call or put prices and comparing coefficients.
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中文摘要：
对数正态分数SABR模型中对数收益率的瞬时波动率是由相关分数布朗运动的指数驱动的。由于驱动布朗运动和分数布朗运动的混合性质，此类模型的概率密度在文献中研究较少。本文给出了对数正态分数阶SABR模型在Fourier空间中关节密度的桥表示。沿着正确选择的确定性路径评估桥表示，得到分数SABR模型概率密度领先阶的小时间渐近展开。通过多次直接推广关节密度表示，可以启发式推导出小时间内关节密度的大偏差原则。通过将拉普拉斯渐近公式应用于买入或卖出价格并比较系数，可以很容易地获得隐含波动率的近似值。
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分类信息：

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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