英文标题：
《Pricing of vanilla and first generation exotic options in the local
stochastic volatility framework: survey and new results》
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作者：
Alexander Lipton, Andrey Gal, and Andris Lasis
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最新提交年份：
2013
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英文摘要：
Stochastic volatility (SV) and local stochastic volatility (LSV) processes can be used to model the evolution of various financial variables such as FX rates, stock prices, and so on. Considerable efforts have been devoted to pricing derivatives written on underliers governed by such processes. Many issues remain, though, including the efficacy of the standard alternating direction implicit (ADI) numerical methods for solving SV and LSV pricing problems. In general, the amount of required computations for these methods is very substantial. In this paper we address some of these issues and propose a viable alternative to the standard ADI methods based on Galerkin-Ritz ideas. We also discuss various approaches to solving the corresponding pricing problems in a semi-analytical fashion. We use the fact that in the zero correlation case some of the pricing problems can be solved analytically, and develop a closed-form series expansion in powers of correlation. We perform a thorough benchmarking of various numerical solutions by using analytical and semi-analytical solutions derived in the paper.
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中文摘要：
随机波动率（SV）和局部随机波动率（LSV）过程可用于模拟各种金融变量的演化，如汇率、股票价格等。人们已经做出了相当大的努力来为写在这些过程控制的基础上的衍生品定价。然而，仍然存在许多问题，包括标准交替方向隐式（ADI）数值方法在解决SV和LSV定价问题上的有效性。一般来说，这些方法所需的计算量非常大。在本文中，我们解决了其中一些问题，并提出了一种可行的替代方法，以替代基于伽辽金-里兹思想的标准ADI方法。我们还以半解析的方式讨论了解决相应定价问题的各种方法。我们利用了在零相关性的情况下，一些定价问题可以解析地解决的事实，并发展了一个封闭形式的相关幂级数展开式。我们使用本文推导的解析解和半解析解对各种数值解进行了全面的基准测试。
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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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