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为了准确描述基础资产波动率的“聚集性”、“杠杆效应”及时变特征,将有偏GARCH模型引入最小二乘蒙特卡罗美式期权定价(LSM)方法中,同时使用Lévy过程修正GARCH模型中的随机数分布,进而表现金融数据的非正态特征和“跳跃”特征,建立了Lévy-GARCH-LSM模型。基于我国13只美式权证、百慕大权证,和S&P 100指数的美式期权的实证研究,发现:(1)Lévy-GARCH模型不仅能精确地描述基础资产的统计特征,而且还提供了较为准确的美式权证定价结果;(2)引入Lévy过程和GARCH模型都能提高权证定价精度,而各类非对称GARCH模型之间没有显著差异;(3)由于我国权证市场交易制度不完善、投机成分严重,与S&P100美式期权的误差相比,基于无套利假设下的Lévy-GARCH模型用以定价我国权证仍存在较大误差。
In order to accurately describe the “aggregation”, “leverage effect” and time-varying features of volatility of underlying assets, the biased GARCH model is introduced into least-squares Monte Carlo pricing method (LSM), and the Lévy process By modifying the distribution of random numbers in GARCH model, and then displaying the non-normal features and the “jump” features of financial data, the Lévy-GARCH-LSM model is established. Based on the empirical study of 13 American warrants, Bermuda warrants and American options of S & P 100 index, we find that: (1) Lévy-GARCH model can not only accurately describe the statistical characteristics of basic assets, but also provide more accurate American warrants (2) The Lévy process and the GARCH model can both improve the pricing accuracy of the warrants, but there is no significant difference between various types of asymmetric GARCH models; (3) Due to the imperfect trading system in China’s warrants market, the speculative component is serious, and S & P100 Compared with the error of American option, the Lévy-GARCH model based on no arbitrage hypothesis still has a big error in pricing warrants in China.