In this research,we summarize the results of a practical study of index options based on the option valuation model which was proposed by Siu and Yang(Acta Math.Appl.Sin.Engl.Ser.,25(3)(2009),pp.339{388),where an EMM ...In this research,we summarize the results of a practical study of index options based on the option valuation model which was proposed by Siu and Yang(Acta Math.Appl.Sin.Engl.Ser.,25(3)(2009),pp.339{388),where an EMM kernel is integrated which takes into account all risk components of a regime-switching model.Further,the regime-switching risk of an economy in the options is priced using a hidden Markov regime-switching model with the risky underlying asset being modulated by a discrete-time,nite-state,hidden Markov chain whose states represent the hidden states of an economy.We apply such a model to the pricing of Hang Seng Index options based on the real-world nancial data from October 2009 to October 2010(i.e.,for the year in which the model was proposed).We employed the entropy martingale measure(EMM)approach proposed by Siu and Yang(Acta Math.Appl.Sin.Engl.Ser.,25(3)(2009),pp.339{388)to determine the optimal martingale measure for the Markov-modulated GBM.In addition,we have proposed a numerical technique called the weighted di erence method to compliment the EMM approach.We have also veri ed the extended jump-di usion model under regime-switching that we proposed recently(Int.J.Finan.Eng.,6(4)(2019),1950038)using the 50ETF options which are obtained from Shanghai Stock Exchange covering a time span from January 2018 to December 2022.Further,we have highlighted the challenges for the EMM kernel-based Markov regime-switching model for pricing the out-of-the-money index options in the real world.展开更多
文摘In this research,we summarize the results of a practical study of index options based on the option valuation model which was proposed by Siu and Yang(Acta Math.Appl.Sin.Engl.Ser.,25(3)(2009),pp.339{388),where an EMM kernel is integrated which takes into account all risk components of a regime-switching model.Further,the regime-switching risk of an economy in the options is priced using a hidden Markov regime-switching model with the risky underlying asset being modulated by a discrete-time,nite-state,hidden Markov chain whose states represent the hidden states of an economy.We apply such a model to the pricing of Hang Seng Index options based on the real-world nancial data from October 2009 to October 2010(i.e.,for the year in which the model was proposed).We employed the entropy martingale measure(EMM)approach proposed by Siu and Yang(Acta Math.Appl.Sin.Engl.Ser.,25(3)(2009),pp.339{388)to determine the optimal martingale measure for the Markov-modulated GBM.In addition,we have proposed a numerical technique called the weighted di erence method to compliment the EMM approach.We have also veri ed the extended jump-di usion model under regime-switching that we proposed recently(Int.J.Finan.Eng.,6(4)(2019),1950038)using the 50ETF options which are obtained from Shanghai Stock Exchange covering a time span from January 2018 to December 2022.Further,we have highlighted the challenges for the EMM kernel-based Markov regime-switching model for pricing the out-of-the-money index options in the real world.
