A transform-based method for pricing Asian options under general two-dimensional models

被引:1
|
作者
Zhang, Weinan [1 ,2 ]
Zeng, Pingping [2 ]
机构
[1] Harbin Inst Technol, Sch Math, Harbin, Peoples R China
[2] Southern Univ Sci & Technol, Dept Math, Shenzhen, Peoples R China
基金
中国国家自然科学基金;
关键词
Arithmetic Asian options; Two-dimensional models; Extended double spiral method; Fast Fourier transform; STOCHASTIC VOLATILITY; BARRIER OPTIONS; EXACT SIMULATION; LEVY PROCESSES; DISCRETE; BOUNDS; FRAMEWORK; VALUATION; ALGORITHM; VARIANCE;
D O I
10.1080/14697688.2023.2256358
中图分类号
F8 [财政、金融];
学科分类号
0202 ;
摘要
We propose a unified transform-based method, which we call the extended double spiral (EDS) method, for pricing arithmetic Asian options under general two-dimensional (2D) models that nest regime-switching Levy models, stochastic volatility (SV) models with Levy jumps, and time-changed Levy models. We first construct a new single backward induction in the state space that relaxes the restriction of the independent increments of the log-asset price. Second, we build an exact and explicit double backward induction in the Fourier space based on this single backward induction, a combination of the 1D Fourier transform method and a key function characterizing the 2D model, and the double spiral method. Third, we develop a unified EDS algorithm to recursively implement this double backward induction via the fast Fourier transform (FFT), various quadrature rules, asymmetric truncation boundaries, and so on. Extensive numerical results across a broad class of 2D models, monitoring frequencies, option moneyness, and model parameters demonstrate that our method is remarkably accurate, efficient, robust, simple to implement, and widely applicable.
引用
收藏
页码:1677 / 1697
页数:21
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