This paper investigates the pricing of discretely sampled variance swaps under a Markov regime-switching jump-diffusion model. The jump diffusion, as well as other parameters of the underlying stock’s dynamics, is modulated by a Markov chain representing different states of the market. A semi-closed-form pricing formula is derived by applying the generalized Fourier transform method. The counterpart pricing formula for a variance swap with continuous sampling times is also derived and compared with the discrete price to show the improvement of accuracy in our solution. Moreover, a semi-Monte-Carlo simulation is also presented in comparison with the two semi-closed-form pricing formulas. Finally, the effect of incorporating jump and regime switching on the strike price is investigated via numerical analysis.

中文翻译：

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马尔可夫调制跳跃扩散模型下的方差掉期定价

本文研究了在马尔可夫政权切换跳跃-扩散模型下离散采样方差掉期的定价。跳跃扩散以及相关股票动态的其他参数由代表市场不同状态的马尔可夫链进行调制。应用广义傅里叶变换法推导了半封闭式定价公式。还推导了具有连续采样时间的方差掉期的对应定价公式，并将其与离散价格进行比较，以显示我们的解决方案准确性的提高。此外，与两个半封闭式定价公式相比，还提供了半蒙特卡洛模拟。最后，通过数值分析研究了结合跳变和状态切换对执行价格的影响。