【作者】 陈聪；

【导师】 唐亚勇；

【作者基本信息】 四川大学 ， 金融数学与计量经济学， 2021， 硕士

【摘要】 随着全球金融市场的深化发展,能满足不同投资者个性化投资需求的各类金融衍生品被设计出来。在众多衍生品中,丰富多样、安全可靠的期权广泛活跃在金融市场中,特别是亚式期权。在经典的Black-Scholes模型被提出后,几何平均亚式期权的解析定价公式被推导出来,但算术平均亚式期权由于其行情价不再服从对数正态分布,无解析定价公式。算术平均半亚式期权是算术平均亚式期权的推广,无解析定价公式。因此在实际中大多采用蒙特卡洛法模拟算法进行定价,但存在定价时间长的问题。本文的研究主要分为五个部分。第一章主要介绍了本文的研究背景、方法和内容。第二章主要简述了本文需要用到的预备知识和基本算法,并给出了每一种基本算法的具体流程。第三章主要推导出了改进蒙特卡洛法和近似半解析法,并通过数值算例发现,近似半解析法在保证精度的前提下,能大幅减少定价时间。第四章主要利用方差缩减技术对近似半解析法进行了改进,并通过数值算例的比较发现,部分新算法定价时间更少、精度更高。第五章主要是本文的一些总结和展望。更多还原

【Abstract】 With the deepening development of the global financial market,various financial derivatives that can meet the individual investment needs of different investors have been designed.Among them,safe and reliable options are widely active in the financial market,especially Asian option.After the classic Black-Scholes model was proposed,the analytical pricing formula of geometric average Asian options was derived.But the arithmetic average Asian option’ s market price no longer obeys the lognormal distribution,there is no analytical pricing formula.The arithmetic average half-Asian option is a generalized Asian option with no analytic pricing formula.In practice,simulation algorithms such as Monte Carlo method is mostly used in option pricing.Although the pricing accuracy is high,the calculation time for pricing is long.This thesis is divided into five chapters.The first chapter introduces the research background,methods and contents of the thesis.The second chapter mainly describes the preparatory knowledge and basic algorithms needed in this thesis,and gives the specific process of each basic algorithm.The third chapter mainly derives the improved Monte Carlo method and the semi-analytic method,and through the comparison of numerical examples,it is found that the semi-analytic method can greatly reduce the pricing time under the premise of ensuring accuracy.The fourth chapter mainly uses the variance reduction technology to improve the semianalytical method,and through the comparison of numerical examples,it is found that some new algorithms take less time to price and have higher accuracy.The fifth chapter is the summary and prospect of this thesis.更多还原