（浙江大学城市学院 杭州 浙江 310012）

【摘要】作为国际金融市场的一种重要基准利率，Libor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；因此，对Libor利率所服从的随机过程选择的准确与否，也就成为对诸多利率衍生证券准确定价的前提条件和关键因素。本文首先基于诸多Libor市场模型改进方法的基础之上，在标准市场模型中加入Heston随机波动率过程，建立随机波动率假设的新型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；最后是实证模拟。研究结论认为，在构建Libor利率动态模型时，若在单因子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。

关键词  Libor市场模型  随机波动率  模型参数校正  MCMC参数估计

中图分类号　F273　　　　文献标识码　A

Theoretic Estimation and Monte Carlo Simulation for Libor Market Interest Rate Models Based on Stochastic Volatility

Ma junhai    Zhang Qiang

(Zhejiang University City College, Hangzhou, Zhejiang, China, 310012)

Abstract: As an important criterion interest rate in international financial market, Libor interest rate has played more and more role in pricing financial assets and managing risk. Therefore, it is very necessary condition and key factor to choose precisely the process for Libor interest rate. 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. Lastly, we make an empirical analysis. The research conclusion is that Libor market model corporated into Heston stochastic volatility can improve greatly the explain ability to interest rate models .

Key words: Libor Market Interest Rate Models; Stochastic Volatility Process; Parameter Calibration; Markov Monte Carlo