This article considers the valuation of digital, barrier, and lookback options in a Markovian, regime-switching, Black–Scholes model. In Fourier space, integral representations for the option prices are derived via the theory on matrix Wiener–Hopf factorizations. Our main focus is on the 2-state case where the matrix Wiener–Hopf factorization is available analytically. A comparison to several numerical alternatives (analytical approximations, the Brownian bridge algorithm and a finite element scheme) demonstrates that the pricing formulas are easy to implement and lead to accurate price estimates.

中文翻译：

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在政权转换经济中对异国期权定价：傅立叶变换法

本文考虑了马尔可夫体制转换Black-Scholes模型中的数字，障碍和回溯选项的估值。在傅立叶空间中，期权价格的积分表示是通过矩阵维纳-霍夫夫分解理论推导出来的。我们的重点是在两态情况下，矩阵Wiener-Hopf因式分解可通过分析获得。与几种数值替代方案（分析近似值，布朗桥算法和有限元方案）的比较表明，定价公式易于实现，并且可以得出准确的价格估算值。