英文标题：
《Fast Quantization of Stochastic Volatility Models》
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作者：
Ralph Rudd, Thomas A. McWalter, Joerg Kienitz, Eckhard Platen
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最新提交年份：
2017
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英文摘要：
Recursive Marginal Quantization (RMQ) allows fast approximation of solutions to stochastic differential equations in one-dimension. When applied to two factor models, RMQ is inefficient due to the fact that the optimization problem is usually performed using stochastic methods, e.g., Lloyd\'s algorithm or Competitive Learning Vector Quantization. In this paper, a new algorithm is proposed that allows RMQ to be applied to two-factor stochastic volatility models, which retains the efficiency of gradient-descent techniques. By margining over potential realizations of the volatility process, a significant decrease in computational effort is achieved when compared to current quantization methods. Additionally, techniques for modelling the correct zero-boundary behaviour are used to allow the new algorithm to be applied to cases where the previous methods would fail. The proposed technique is illustrated for European options on the Heston and Stein-Stein models, while a more thorough application is considered in the case of the popular SABR model, where various exotic options are also priced.
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中文摘要：
递归边际量化（RMQ）允许快速逼近一维随机微分方程的解。当应用于双因素模型时，RMQ效率低下，因为优化问题通常使用随机方法执行，例如Lloyd算法或竞争学习矢量量化。本文提出了一种新的算法，将RMQ应用于双因素随机波动率模型，保留了梯度下降技术的效率。与当前的量化方法相比，通过对波动过程的潜在实现进行微调，计算工作量显著减少。此外，还使用了建模正确零边界行为的技术，以便将新算法应用于先前方法可能失败的情况。所提议的技术在Heston和Stein-Stein模型上对欧洲期权进行了说明，而在流行的SABR模型中考虑了更全面的应用，其中还对各种奇异期权进行了定价。
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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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