TY - JOUR
T1 - Empirical Study on Option Pricing under Markov Regime Switching Economics
AU - Liu , Lianfeng (David)
JO - Annals of Applied Mathematics
VL - 1
SP - 21
EP - 42
PY - 2024
DA - 2024/02
SN - 40
DO - http://doi.org/10.4208/aam.OA-2023-0012
UR - https://global-sci.org/intro/article_detail/aam/22926.html
KW - Option pricing, EMM, regime-switching, hidden Markov model, Esscher
transform, weighted difference method.
AB - <p style="text-align: justify;">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, finite-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 financial 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 difference method to compliment the EMM approach. We
have also verified the extended jump-diffusion 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.</p>