英文标题：
《Modelling the skew and smile of SPX and DAX index options using the
Shifted Log-Normal and SABR stochastic models》
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作者：
Jan Kuklinski, Doinita Negru and Pawel Pliszka
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最新提交年份：
2014
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英文摘要：
We discuss modelling of SPX and DAX index option prices using the Shifted Log-Normal (SLN) model, (also known as Displaced Diffusion), and the SABR model. We found out that for SPX options, an example of strongly skewed option prices, SLN can produce a quite accurate fit. Moreover, for both types of index options, the SLN model is giving a good fit of near-at-the-forward strikes. Such a near-at-the-money fit allows us to calculate precisely the skew parameter without involving directly the 3rd moment of the related probability distribution. Eventually, we can follow with a procedure in which the skew is calculated using the SLN model and further smile effects are added as a next iteration/perturbation. Furthermore, we point out that the SLN trajectories are exact solutions of the SABR model for rho = +/-1.
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中文摘要：
我们使用移位对数正态（SLN）模型（也称为置换扩散）和SABR模型讨论SPX和DAX指数期权价格的建模。我们发现，对于SPX期权，一个强烈倾斜期权价格的例子，SLN可以产生一个非常精确的拟合。此外，对于这两种类型的指数期权，SLN模型都能很好地拟合近距离正向攻击。这样的近似货币拟合允许我们精确计算倾斜参数，而不直接涉及相关概率分布的第三阶矩。最后，我们可以使用SLN模型计算倾斜，并在下一次迭代/扰动时添加进一步的微笑效果。此外，我们还指出，对于rho=+/-1，SLN轨迹是SABR模型的精确解。
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分类信息：

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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