广西师范大学学报（自然科学版） ›› 2016, Vol. 34 ›› Issue (3): 74-85.doi: 10.16088/j.issn.1001-6600.2016.03.011

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基于仿射跳扩散模型的利率衍生品定价

汪嘉骎, 邓国和   

  1. 广西师范大学数学与统计学院,广西桂林541004
  • 收稿日期:2016-03-01 出版日期:2016-09-30 发布日期:2018-09-17
  • 通讯作者: 邓国和(1969—),男,湖南桂阳人,广西师范大学教授,博士. E-mail:dengguohe@mailbox.gxnu.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(11461008);教育部人文社会科学研究规划基金资助项目(13YJA910003);广西自然科学基金资助项目(2013GXNSFAA019005);广西高等学校科学技术研究重点项目(2013ZD010)

Pricing of Interest Rate Derivatives Based on Affine Jump Diffusion Model

WANG Jiaqin, DENG Guohe   

  1. School of Mathematics and Statistics,Guangxi Normal University, Guilin Guangxi 541004, China
  • Received:2016-03-01 Online:2016-09-30 Published:2018-09-17

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摘要： 本文考虑短期利率满足一类仿射跳扩散期限结构模型的利率衍生品定价。应用Fourier变换方法和远期测度技术,获到了零息票债券及基于零息票债券为标的资产的欧式债券期权价格的显示解,并将此结果应用于付息债券期权和利率期权的定价。最后,利用数值实例分别分析了债券和零息票债券期权价格受利率模型中各主要参数的影响,以及期权的隐含波动率问题。数值结果表明,跳跃风险参数对利率衍生品价格和隐含波动率有显著作用,这也验证了仿射跳扩散的利率期限结构模型具有较好拟合实际的能力。

关键词: 仿射跳扩散模型, 利率期限结构, 债券期权, Fourier变换, 隐含波动率

Abstract: The pricing of interest rate derivatives is considered under an affine jump diffusion model. Using the Fourier transform method and the forward measure change technique,the closed explicit formulas for both the price of the default-free,zero-coupon bond and the value of the European options on the default-free,zero-coupon bond are obtained. Furthermore,pricing problems on both the European option on the coupon bond and the interest rate options are extended in this model by applying these explicit formulas above. Finally,the impacts of the key parameters in this model on prices for both the bond and bond option,and implied volatilities of bond options are analyzed by numerical examples,respectively. Numerical results show that the jump risks have more remarkable effects on the interest rate derivative prices and implied volatility,which show that the affine jump diffusion term structure model of the interest rate fits reality well.

Key words: affine jump diffusion model, term structure of interest rate, bond options, Fourier transform, implied volatility.

中图分类号: 

  • O211.9
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