基于Libor模型的百慕大互换期权定价及其校准  

Bermudan Swaption Pricing and Calibration Based on Libor Market Model

作　　者：宋斌 王斯燕 SONG Bin;WANG Siyan(Investment Department, School of Management Science and Engineering, Central University of Finance and Economics, Beijing 100081)

机构地区：[1]中央财经大学管理科学与工程学院投资系

出　　处：《系统科学与数学》2018年第3期334-347,共14页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(11301560);教育部人文社会科学研究规划基金(14YJA790048)资助课题

摘　　要：由于Libor市场模型是直接对市场上可观测的利率建模,省去了由瞬时远期利率和市场利率之间转换的过程,因此文章选择Libor市场模型定价百慕大互换期权,并选择最小二乘蒙特卡罗方法处理提前实施特征.在模型校准方面,Libor市场模型中互换期权的隐含波动率与远期Libor的波动率之间存在封闭解关系,从而提高了校准的效率和精度.论文通过固定到期日的欧式互换期权对Libor市场模型进行了校准.经过校准,欧式互换期权隐含波动率与其相应市场报价间的均方误差从1198.04%降到了4.63%,取得了较好的校准效果.最后,用经过校准的参数定价百慕大互换期权,并与敲定利率相同的欧式互换期权定价结果进行对比,发现相同敲定利率的两种期权,百慕大互换期权的价格要明显高于欧式互换期权,符合逻辑判断,侧面验证了定价和校准结果的准确性.Since Libor market model（LMM） is modelling the observable interest rate and avoiding the transformation process from instantaneous forward rate to market interest rate, LMM is chosen for Bermudan swaption pricing and employed Least-Squared Monte Carlo to deal with early-exercise characteristics. About the model calibration, the implied volatility of swaption in Libor market model exists closed-form solution relationship with forward Libor＇s volatility, which can improve the calibration＇s efficiency and accurancy. The paper adopts the fixed maturity European swaption to calibrate Libor market model. After the calibration, MSE between the implied volatility of European swaption and the related market quote decreases from 1198.04% to 4.63% and shows better calibration effect. At last, the calibrated parameters is employed for Bermudan swaption pricing and compared with the results European swaption with same strike interest rate. The results show that the Bermudan swaption＇s price is obviously higher than the related European swaption and validate the pricing method and calibration＇s correctness in some degree.

关 键 词：Libor市场模型 百慕大互换期权 最小二乘蒙特卡罗 欧式互换期权 

分 类 号：F224[经济管理—国民经济] F830.9