LQ45指数长期期权策略的Black-Scholes模型与GARCH模型比较

Riko Hendrawan, Abdul Safar
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摘要

本研究使用1998年至2021年的收盘价数据,比较了应用于LQ45指数的长期勒死策略中的Black-Scholes模型和GARCH模型。它旨在评估收益,计算危机时期和非危机时期的回报,并通过平均均方误差(AMSE)评估绩效。布莱克-斯科尔斯模型在一个月和三个月期权上的表现一直优于GARCH。一个月期权的平均回报率为28.64%,三个月期权的平均回报率为43.31%。在危机期间,布莱克-斯科尔斯一个月期权的平均利润为43.36%,三个月期权的平均利润为45.14%。在非危机情况下,一个月期权的平均利润为26%,三个月期权的平均利润为42.84%。模型性能因期权类型和市场环境而异。Black-Scholes在一个月看涨期权方面表现出色(误差1.268%),而GARCH在一个月看跌期权方面表现较好(误差1.0981%)。三个月期权方面,GARCH表现优于看涨期权(误差1.270%),Black-Scholes表现优于看跌期权(误差3.117%)。总之,在模型之间的选择应该考虑市场条件,在危机情况下倾向GARCH,在非危机情况下倾向Black-Scholes。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Comparing Black-Scholes and GARCH Models in Long Strangle Option Strategies for LQ45 Index
This study compared the Black-Scholes and GARCH models in a long strangle strategy applied to the LQ45 index using closing price data from 1998 to 2021. It aimed to assess the benefits, calculate returns during crises and non-crisis periods, and evaluate performance through Average Mean Square Error (AMSE). The Black-Scholes model consistently outperformed GARCH in one- and three-month options. One-month options had an average return of 28.64%, and three-month options, 43.31%. In crises, Black-Scholes delivered average profits of 43.36% for one-month and 45.14% for three-month options. In non-crisis conditions, profits averaged 26% for one-month and 42.84% for three-month options. Model performance varied by option type and market context. Black-Scholes excelled in one-month call options (1.268% error), while GARCH performed better in one-month put options (1.0981% error). For three-month options, GARCH outperformed in call options (1.270% error), and Black-Scholes dominated put options (3.117% error). In summary, the choice between models should consider market conditions, favoring GARCH during crises and Black-Scholes in non-crisis scenarios.
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