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Fourier Method for Valuation of Options under Parameter and State Uncertainty
The Journal of Derivatives ( IF 0.647 ) Pub Date : 2019-09-27 , DOI: 10.3905/jod.2019.1.085
Erik Lindström

Mainstream option valuation theory relies implicitly on the assumption that latent states (such as stochastic volatility) and parameters are perfectly known, an assumption that is dubious in many ways. Computing the value of options under the assumption of perfect knowledge will typically introduce bias. Correcting for the bias is straightforward but can be computationally expensive. Fourier-based methods for computing option values are nowadays the preferred computational technique in the financial industry as a result of speed and accuracy. The author shows that the bias correction for parameter and state uncertainty for a large class of processes can be incorporated into the Fourier framework, resulting in substantial computational savings compared with Monte Carlo methods or deterministic quadrature rules previously used. In addition, the author proposes extensions, such as time varying parameters and hyperparameters, to the class of uncertainty models. The author finds that the proposed Fourier method is retaining all the good properties that are associated with Fourier methods; it is fast, accurate, and applicable to a wide range of models. Furthermore, the empirical performance of the corrected models is almost uniformly better than that of their noncorrected counterparts when evaluated on S&P 500 option data. TOPICS: Derivatives, options, factor-based models, analysis of individual factors/risk premia Key Findings • Parameter and state uncertainty in option models is often ignored but this leads to bias. • The bias correction introduced in this paper can be computed through the standard Fourier methodology, being fast and accurate. • The methodology results in better model in-sample and out-of-sample for a wide range of models, and the best results are found for parameters where the uncertainty is substantial.

中文翻译:

参数和状态不确定性下期权定价的傅里叶方法

主流期权估值理论隐含地依赖于假设,即潜伏状态(例如随机波动性)和参数是众所周知的,这一假设在许多方面都令人怀疑。在完全知识的假设下计算期权的价值通常会引入偏差。校正偏差很简单,但是在计算上可能会很昂贵。由于速度和准确性,如今基于傅里叶的期权价值计算方法已成为金融行业的首选计算技术。作者表明,可以将大量过程的参数和状态不确定性的偏差校正纳入傅里叶框架,与之前使用的蒙特卡洛方法或确定性正交规则相比,可节省大量计算量。此外,作者提议将不确定性模型的类别扩展,例如时变参数和超参数。作者发现,所提出的傅里叶方法保留了与傅里叶方法相关的所有优良特性。它快速,准确,适用于各种型号。此外,在对标准普尔500期权数据进行评估时,校正后的模型的经验性能几乎均优于未校正后的模型。主题:衍生工具,期权,基于因子的模型,单个因子/风险溢价的分析主要发现•期权模型中的参数和状态不确定性通常被忽略,但这会导致偏差。•本文中介绍的偏差校正可以通过标准的傅立叶方法进行计算,既快速又准确。
更新日期:2019-09-27
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