随机波动率LIBOR模型及其结构性存款定价:理论估计与蒙特卡罗模拟

Stochastic volatility LIBOR market model and its structured deposits pricing:Theoretic estimation and Monte Carlo simulation

LIBOR市场利率已经在金融资产定价和风险度量中发挥着越来越重要的作用,而以其为标的利率的外汇结构性存款也得到了广泛应用.因此,对LIBOR利率动态过程及其结构性存款定价进行有效理论估计和模拟计算则显得尤为重要.本文首先在标准市场模型中加入Heston随机波动率过程,建立随机波动率过程驱动的新型LIBOR市场模型;其次,运用Black逆推参数校正方法和MCMC参数估计方法对该LIBOR利率市场模型中的局部波动率和随机波动率过程中的参数进行校正和估计;再次,基于最优基本函数改进的LSM方法对可赎回外汇结构性存款定价进行模拟计算;最后是实证分析.研究结论认为:在单因子LIBOR利率市场模型基础上引入随机波动率过程,则可大大地提高利率模型的解释力;基于最优基本函数改进的LSM定价方法所得结果更接近于实际利率下所求理论价值.

LIBOR market model has played more and more important role in pricing financial assets and managing risk. FX structured deposits driven by LIBOR interest rate also have get more and more application. Therefore, it is very necessary to make theoretic estimation and Monte Carlo simulation for LIBOR interest rate process and its FX structured deposits pricing. In this paper firstly, on the basic of many existing improved methods for LIBOR market models, combining Heston stochastic volatility into standard market models, we set up a new LIBOR market model. Secondly, by using of Black inverse parameters calibrating methods and Markov chain Monte Carlo simulation, we calibrate and estimate parameters of the new LIBOR market models. Thirdly, we use the improvement LSM to price this FX structured product. Lastly, we make an empirical analysis. The research conclusions are： 1） LIBOR market model with the stochastic volatility process can describe the LIBOR rate very well and display a finer accuracy. 2） The improvement LSM can get the much more precise result.