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首页> 外文期刊>IEEE transactions on industrial informatics >European Option Pricing With a Fast Fourier Transform Algorithm for Big Data Analysis
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European Option Pricing With a Fast Fourier Transform Algorithm for Big Data Analysis

机译：具有快速傅里叶变换算法的大数据分析欧洲期权定价

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摘要

Several empirical studies show that, under multiple risks, markets exhibit many new properties, such as volatility smile and cluster fueled by the explosion of transaction data. This paper attempts to capture these newly developed features using the valuation of European options as a vehicle. Statistical analysis performed on the data collected from the currency option market clearly shows the coexistence of mean reversion, jumps, volatility smile, and leptokurtosis and fat tail. We characterize the dynamics of the underlying asset in this kind of environment by establishing a coupled stochastic differential equation model with triple characteristics of mean reversion, nonaffine stochastic volatility, and mixed-exponential jumps. Moreover, we propose a characteristic function method to derive the closed-form pricing formula. We also present a fast Fourier transform (FFT) algorithm-based numerical solution method. Finally, extensive numerical experiments are conducted to validate both the modeling methodology and the numerical algorithm. Results demonstrate that the model behaves well in capturing the properties observed in the market, and the FFT numerical algorithm is both accurate and efficient in addressing large amount of data.
机译：几项实证研究表明，在多重风险下，市场表现出许多新特性，例如波动性微笑和交易数据爆炸推动的集群。本文尝试使用欧洲期权的评估工具来捕捉这些新开发的功能。对从货币期权市场收集的数据进行的统计分析清楚地表明了均值回归，跳跃，波动性微笑以及瘦态和肥尾现象的并存。通过建立具有均值回归，非仿射随机波动率和混合指数跳跃三重特征的耦合随机微分方程模型，我们可以表征这种环境下基础资产的动态。此外，我们提出了一种特征函数方法来推导封闭式定价公式。我们还提出了一种基于快速傅立叶变换（FFT）算法的数值求解方法。最后，进行了广泛的数值实验，以验证建模方法和数值算法。结果表明，该模型在捕获市场观察到的属性方面表现良好，并且FFT数值算法在处理大量数据方面既准确又有效。

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