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**A new exact solution for pricing European options in a two-state regime-switching economy.**
*(English)*
Zbl 1268.91170

Summary: We derive a new exact solution for pricing European options in a two-state regime-switching economy. Two coupled Black-Scholes partial differential equations (PDEs) under the regime switching are solved using the Fourier Transform method. A key feature of the newly-derived solution is its simplicity in the form of a single integral with a real integrand, which leads to great computational efficiency in comparison with other closed-form solutions previously presented in the literature. Numerical examples are provided to demonstrate some interesting results obtained from our pricing formula.

### MSC:

91G20 | Derivative securities (option pricing, hedging, etc.) |

35Q91 | PDEs in connection with game theory, economics, social and behavioral sciences |

### Keywords:

regime switching; European options; Fourier transform; Fourier inversion; Black-Scholes model
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\textit{S.-P. Zhu} et al., Comput. Math. Appl. 64, No. 8, 2744--2755 (2012; Zbl 1268.91170)

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