时变分数布朗运动下的GARCH族欧式期权定价研究  

The family of GARCH European option pricing model under the fractional Brownian motion with time-varying Hurst index

作　　者：史永东[1] 程航 王光涛 

机构地区：[1]东北财经大学应用金融研究中心和金融学院,大连116025 [2]信和惠民投资管理(北京)有限公司,北京100022

出　　处：《系统工程理论与实践》2017年第10期2527-2538,共12页Systems Engineering-Theory & Practice

基　　金：国家自然科学基金(71471031;71171036);国家社会科学基金重点项目(14AZD089);辽宁特聘教授支持计划(辽教发[2013]204号);教育部人文社会科学研究一般项目(15YJA790092;15YJC790041)~~

摘　　要：本文拓展了分数布朗运动理论下欧式期权定价问题,尤其突破了Hurst指数和波动率为常数的假设.我们在时变Hurst指数的分数布朗运动环境下,采用GARCH族模型描述收益率序列的波动率,推导出了一个欧式看涨期权定价的闭型解.利用该模型和韩国Kospi200股指期权日交易数据的实证检验表明,韩国Kospi200股指波动率符合GJR过程,时变波动率下的分数布朗运动刻画金融市场的动态特征比采用标准布朗运动更适合,该模型计算的期权理论价格与市场价格更接近,优于传统的定价模型.This paper extends the theory of the European option pricing under fractional Brownian motion, particularly breaking the assumptions that the Hurst index and volatility are constant. When the Hurst index of fractional Brownian motion is time varying, with using the GARCH model to describe the volatility of yields sequence we can deduce a closed type solution of the European call option pricing. Using this model and the day trading data of the Korean stock index options Kospi200, the empirical test suggest that the volatility of Kospi200 is followed the G JR process. The time-varying volatility under the fractional Brownian motion that can describe the dynamic characteristics of the financial market is more suitable than the standard Brownian motion. The option theory prices of this model is closer to the market price, which is better than the traditional pricing model.

关 键 词：分数布朗运动 随机分析 GARCH模型 期权定价 

分 类 号：F830.2[经济管理—金融学]