英文标题：
《Quantization goes Polynomial》
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作者：
Giorgia Callegaro and Lucio Fiorin and Andrea Pallavicini
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最新提交年份：
2019
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英文摘要：
Quantization algorithms have been successfully adopted to option pricing in finance thanks to the high convergence rate of the numerical approximation. In particular, very recently, recursive marginal quantization has been proven to be a flexible and versatile tool when applied to stochastic volatility processes. In this paper we apply for the first time quantization techniques to the family of polynomial processes, by exploiting their peculiar nature. We focus our analysis on the stochastic volatility Jacobi process, by presenting two alternative quantization procedures: the first is a new discretization technique, whose foundation lies on the polynomial structure of the underlying process and which is suitable for vanilla option pricing, the second is based on recursive marginal quantization and it allows for pricing of (vanilla and) exotic derivatives. We prove theoretical results to assess the induced approximation errors, and we describe in numerical examples practical tools for fast vanilla and exotic option pricing.
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中文摘要：
由于数值逼近的高收敛速度，量化算法已成功应用于金融期权定价。特别是最近，当应用于随机波动过程时，递归边际量化已被证明是一种灵活和通用的工具。本文利用多项式过程的特殊性质，首次将量化技术应用于多项式过程族。我们重点分析了随机波动率Jacobi过程，提出了两种可选的量化方法：第一种是一种新的离散化技术，其基础是基础过程的多项式结构，适用于普通期权定价，第二种是基于递归边际量化，允许对（普通和）外来衍生品进行定价。我们证明了评估诱导近似误差的理论结果，并在数值示例中描述了快速普通和奇异期权定价的实用工具。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Pricing of Securities 证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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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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