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          林莎:A regime switching fractional Black–Scholes model and European option pricing
          發布日期:2020-08-29 閱讀:255 次

          《Communications in Nonlinear Science and Numerical Simulation》 2020, 85: 105222

          摘要:European option pricing is considered under a regime switching FMLS model. • A two-step solution procedure is developed to solve the coupled FPDE system. • An exact and explicit pricing formula is presented based on Fourier cosine series. In this paper, we investigate the European option pricing problem under a regime switching FMLS (finite moment log-stable) model. This model is not only able to capture the main characteristics of asset returns, it also incorporates the effect of regime switching being consistent with market observations. However, option prices under this model are governed by a coupled FPDE (fractional partial differential equation) system, and the difficulty in seeking for analytical solution arises from the combination of the coupled system and the spatial-fractional derivative. To deal with this difficulty, we develop a two-step solution procedure; we firstly assume that the future information of the Markov chain is known, and we derive the conditional option price by analytically solving a time dependent FPDE, based on which an exact and explicit pricing formula for the unconditioned price is successfully worked out by using the Fourier cosine series expansion. It is also shown through the numerical experiments that it converges very rapidly and has potential to be applied in practice.