基于随机利率模型可转换债券定价分析

Analyzing pricing of convertible bonds with stochastic interest rate modelling

基于债券数据利用正则化方法给出了均值函数随机利率模型的参数估计,进一步应用D'Yakonov分裂方法构造了稳定的差分格式并对可转换债券定价问题进行数值计算.数值结果表明常数均值和相应的均值函数随机利率模型对可转换债券价格的影响没有显著的差异,然而比较高斯和非高斯利率模型(包括引入长期均值函数)所得的可转换债券价格很明显地依赖于利率的期限结构.因此,在定价可转换债券过程中,需要考虑不同期限结构的利率模型对可转换债券价格的影响,但无需引入均值函数.

This paper develops a parametric estimation for the time-varying mean stochastic interest model by using regularization method. Furthermore, the price of convertible bond could be computed by using the D’Yakonov splitting method together with stable finite difference scheme. The numerical results show that the prices of convertible bonds are not significantly different when using the stochastic interest rate model and the extended model. However, the prices of convertible bonds are highly sensitive to the term structure of Gaussian and Non-Gaussian interest rate model, including the extended model. These results imply that it is important to consider the effects of different term structure models in valuing convertible bonds, but not necessary to consider the mean function.