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Lewis Model Revisited: Option Pricing with Lévy Processes
Bulletin of the Malaysian Mathematical Sciences Society ( IF 1.2 ) Pub Date : 2020-09-26 , DOI: 10.1007/s40840-020-01025-3
Mehmet Fuat Beyazit , Kemal Ilgar Eroglu

This paper aims to discuss the mathematical details in Lewis’ model by considering the analyticity and integrability conditions of characteristic functions and payoff functions of contingent claims. In his seminal paper, Lewis shows that it is much easier to compute the option value in the Fourier space than computing in terminal security price space. He computes the option value as an integral in the Fourier space, the integrand being some elementary functions and the characteristic functions of a wide range of Lévy processes. The model also illustrates how the residue calculus leads to several variations of option formulas through the contour integrals. In this paper, we provide with, to a reasonable extent, some rigor into the mathematical background of Lewis’ model and validate his results for particular Lévy processes. We also simply give the analyticity conditions for the characteristic function of the Carr–Geman–Madan–Yor model and a simple derivation of the characteristic function of Kou’s double exponential model.



中文翻译:

再论Lewis模型:带有Lévy流程的期权定价

本文旨在通过考虑或有债权的特征函数和收益函数的解析性和可积性条件,讨论刘易斯模型中的数学细节。Lewis在开创性的论文中指出,在傅立叶空间中计算期权价值比在终端安全价格空间中计算容易得多。他将期权价值作为傅立叶空间中的一个积分进行计算,该积分是一些Lévy过程的一些基本函数和特征函数。该模型还说明了残差演算如何通过轮廓积分导致期权公式的几种变化。在本文中,我们在合理范围内为刘易斯模型的数学背景提供了一些严格的条件,并针对特定的Lévy过程验证了他的结果。

更新日期:2020-09-26
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