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对一般的Markov调制Lévy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 Lévy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.
For the general Markov-modulated Lévy model, the method of Fourier Cosine series expansion is used to get the price of European option. Furthermore, in order to improve the calculation accuracy of Fourier Cosine series expansion method, the object of Fourier Cosine series expansion is modified , The method of calculating the modified Fourier Cosine series expansion of the European option price is obtained.In addition, the method is also applied to the calculation of the option pricing of the Markov modulated Black-Scholes model, the Markov modulated Merton jump diffusion model and the Markov modulated CGMY Lévy model. The numerical calculation shows that the modified Fourier Cosine series expansion method should be slower than the Fourier Cosine series expansion method, but the accuracy is greatly improved. Especially for Markov modulation pure jump model, the effect is more For the obvious.