目前关于利率波动率指数的研究是在利率衍生品价格模型的基础上构造的,为了进一步扩展利率隐含波动率指数的应用范围,在利率波动模型的基础上研究收益率数据信息中隐含的随机波动率的性质。基于2021年1月至2023年2月的国债收益率数据,通过马尔可夫链蒙特卡罗(Markov chain Monte Carlo,MCMC)模型对收益率数据进行建模分析。结果表明:在收益率为基础的利率波动率模型中,长期利率的波动性明显低于短期利率的。本文使用国债收益率作为基础数据,相较于期权市场中的波动率指数,本文的模型不受期权市场上期权种类以及规模的影响,具有更大的适用范围。
In this paper,we incorporate Markov regime-switching into a two-factor stochastic volatility jump-diffusion model to enhance the pricing of power options.Furthermore,we assume that the interest rates and the jump intensities of the assets are stochastic.Under the proposed framework,first,we derive the analytical pricing formula for power options by using Fourier transform technique,Esscher transform and characteristic function.Then we provide the efficient approximation to calculate the analytical pricing formula of power options by using the FFT approach and examine the accuracy of the approximation by Monte Carlo simulation.Finally,we provide some sensitivity analysis of the model parameters to power options.Numerical examples show this model is suitable for empirical work in practice.
