模糊调适性遗传程序规划在认购权证评价模式之应用

Study of Warrants Pricing Based on Fuzzy Genetic Programming

近几年来由于国际金融的快速发展,为了因应金融环境变动的需要,金融商品不断创新,市场亦持续开拓。回顾台湾金融商品市场也如此,其中又以认购权证的发展最为快速蓬勃。多数人在评价权证时,仍采用Black-Scholes的选择权评价模式,属于模式驱动理论的Black-Scholes必须建立在许多前提假设下,然而这些假设与真实世界是不尽相符的,使得此模型在实际运作上易产生价格偏误的现象。因此,该研究应用遗传程序规划,其符合资料驱动理论无母数方法的特质,具有强大的平行搜寻能力,可以描述复杂非线性的权证价格。此外,还设计模糊的交配率与突变率,并在演化过程中对其进行动态地调整。结果显示,使用模糊逻辑控制单元的遗传程序规划与固定参数的遗传程序规划相比,演化初期拥有较佳的利用力以达到快速的收敛,而在演化后期则拥有较好的探索能力,较易从区域最佳解跳脱出来,模糊控制单元对其整体搜寻全域最佳解能力有着不错的助益,同时在订价精确度上优于BS模式。

The traditional approach to pricing a derivative security (warrants pricing) is BS model pioneered by Black and Scholes .This model adopts model-driven approach with many assumptions, which are often not met in the real world and produce pricing bias. Therefore, this paper used Fuzzy Genetic Programming (FGP) model, which belong to data-driven approach, to price warrants. They are nonparametric, and have strong abilities in horizontal searching. Thus the complex nonlinear warrants pricing can describe by these models. The fuzzy crossover rate and mutation rate are adopted in these methods to show dynamic regulation of the evolution processes. Finally, the result of the experiment is shown as following: (1) The FGP has better searching abilities than the fixed parameter GP and the better precision of pricing than the BS model. (2) The FGP is more suitable to basket warrants than individual warrants in predicting prices. (3) If the predictive bias near the pay time is large, the period will raise the predictive accuracy of the FGP. (4) The simulation of investment strategy by the FGP is better than traditional GP model.