TY - JOUR ID - 12707 TI - Stochastic analysis and invariant subspace method for handling option pricing with numerical simulation JO - Computational Methods for Differential Equations JA - CMDE LA - en SN - 2345-3982 AU - Hejazi, Reza AU - Dastranj, Elham AU - Habibi, Noora AU - Naderifard, Azadeh AD - Faculty of mathematical sciences, Shahrood university of technology, Shahrood, Semnan, Iran. Y1 - 2022 PY - 2022 VL - 10 IS - 2 SP - 419 EP - 430 KW - Option pricing KW - Markov chain KW - Geometric Brownian motion KW - finite difference method DO - 10.22034/cmde.2021.38468.1692 N2 - In this paper, option pricing is given via stochastic analysis and invariant subspace method. Finally numerical solutions is driven and shown via diagram. The considered model is one of the most well known non-linear time series model in which the switching mechanism is controlled by an unobservable state variable that follows a first-order Markov chain. Some analytical solutions for option pricing are given under our considered model. Then numerical solutions are presented via finite difference method.  UR - https://cmde.tabrizu.ac.ir/article_12707.html L1 - https://cmde.tabrizu.ac.ir/article_12707_f94c97ceb397384b05b4a404ceb7e6d0.pdf ER -