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摘要翻译：
在本工作中，我们详细介绍了计算高维积分的快速卷积算法在乘性噪声随机过程中的应用。该算法给出了任意时刻条件概率密度函数的数值解，并成功地应用于二次线性扩散过程和分段线性扩散过程。金融收益时间序列的统计特征，如尾部厚度和标度特性的再现能力，使得这一过程在期权定价中具有吸引力。由于缺乏精确的分析结果，我们利用快速卷积作为一种数值方法替代蒙特卡罗模拟在客观和风险中立的情况下。在数值部分中，我们记录了卷积在速度和效率方面超过蒙特卡罗的速度。
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英文标题：
《Multiplicative noise, fast convolution, and pricing》
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作者：
Giacomo Bormetti and Sofia Cazzaniga
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最新提交年份：
2011
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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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英文摘要：
In this work we detail the application of a fast convolution algorithm computing high dimensional integrals to the context of multiplicative noise stochastic processes. The algorithm provides a numerical solution to the problem of characterizing conditional probability density functions at arbitrary time, and we applied it successfully to quadratic and piecewise linear diffusion processes. The ability in reproducing statistical features of financial return time series, such as thickness of the tails and scaling properties, makes this processes appealing for option pricing. Since exact analytical results are missing, we exploit the fast convolution as a numerical method alternative to the Monte Carlo simulation both in objective and risk neutral settings. In numerical sections we document how fast convolution outperforms Monte Carlo both in velocity and efficiency terms.
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PDF链接：
https://arxiv.org/pdf/1107.1451
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