中文摘要：

对一般的Markov调制L′evy模型，利用Fourier Cosine级数展开原理得到欧式期权价格的计算方法。进一步，为了改进期权定价的Fourier Cosine级数展开方法的计算精度， Fourier Cosine级数展开的对象进行了修正，获得了欧式期权价格的修正Fourier Cosine级数展开计算方法。此外，还将获得的方法应用于Markov调制Black-Scholes模型， Markov调制Merton跳扩散模型和Markov调制CGMY L′evy模型期权定价的计算。具体的数值计算说明：修正Fourier Cosine级数展开方法应与Fourier Cosine级数展开方法相比，收敛速度要慢一些，但准确性却有很大的提高。特别是对Markov调制纯跳模型，效果更为显著。

英文摘要：

A method of calculating price of European options is obtained via Fourier-Cosine expansions approach when the underlying asset price follows a very general state-dependent regime-switching Levy process. Furthermore, in order to improve accurate of the Fourier-Cosine expansions, a modified Fourier-Cosine expansions is developed. The method is then applied to option pricing for European options in Black-Scholes model, Merton jump diffusion model and CGMY L′evy model, all with Markov regime switching. Numerical results illustrate that although the convergence rate of method modified Fourier-Cosine expansions is slower than that of Fourier-Cosine expansions, accuracy of method of modified Fourier-Cosine expansions is greatly improved. In particular for case of CGMY L′evy model, the improvement is significant.