英文标题：
《Fast calibration of two-factor models for energy option pricing》
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作者：
Emanuele Fabbiani, Andrea Marziali, Giuseppe De Nicolao
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最新提交年份：
2020
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英文摘要：
  Energy companies need efficient procedures to perform market calibration of stochastic models for commodities. If the Black framework is chosen for option pricing, the bottleneck of the market calibration is the computation of the variance of the asset. Energy commodities are commonly represented by multi-factor linear models, whose variance obeys a matrix Lyapunov differential equation. In this paper, analytical and numerical methods to derive the variance are discussed: the Lyapunov approach is shown to be more straightforward than ad-hoc derivations found in the literature and can be readily extended to higher-dimensional models. A case study is presented, where the variance of a two-factor mean-reverting model is embedded into the Black formulae and the model parameters are calibrated against listed options. The analytical and numerical method are compared, showing that the former makes the calibration 14 times faster. A Python implementation of the proposed methods is available as open-source software on GitHub.
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中文摘要：
能源公司需要高效的程序来执行商品随机模型的市场校准。如果选择黑色框架进行期权定价，市场校准的瓶颈是资产方差的计算。能源商品通常由多因素线性模型表示，其方差服从矩阵李亚普诺夫微分方程。本文讨论了推导方差的分析和数值方法：李雅普诺夫方法比文献中的特殊推导更为简单，并且可以很容易地扩展到高维模型。给出了一个案例研究，其中将双因素均值回复模型的方差嵌入到Black公式中，并根据列出的选项校准模型参数。对解析法和数值法进行了比较，结果表明前者使标定速度提高了14倍。GitHub上的开源软件提供了所提议方法的Python实现。
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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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