短期利率模型中隐含波动率的重构

doi:10.13371/j.cnki.chin.q.j.m.2017.04.006

数学季刊 ›› 2017, Vol. 32 ›› Issue (4): 395-406.doi: 10.13371/j.cnki.chin.q.j.m.2017.04.006

短期利率模型中隐含波动率的重构

1. School of Mathematics and Statistics, Shandong Normal University2. School of Information, Renmin University of China

收稿日期:2015-07-07 出版日期:2017-12-30 发布日期:2020-10-20
作者简介:ZHAO Fang-fang(1986-), female, native of Xintai, Shandong, a lecturer of Shandong Normal University, Ph.D., engages in inverse problems and computation in ¯nance; XU Zuo-liang(1965-), male, native of Xinjin, Liaoning, a professor of Renmin University of China, Ph.D., engages in inverse problems and their applications, computation in ¯nance.
基金资助:
Supported by the National Natural Science Foundation of China(11171349)；

Recover Implied Volatility in Short-term Interest Rate Model

1. School of Mathematics and Statistics, Shandong Normal University2. School of Information, Renmin University of China

Received:2015-07-07 Online:2017-12-30 Published:2020-10-20
About author:ZHAO Fang-fang(1986-), female, native of Xintai, Shandong, a lecturer of Shandong Normal University, Ph.D., engages in inverse problems and computation in ¯nance; XU Zuo-liang(1965-), male, native of Xinjin, Liaoning, a professor of Renmin University of China, Ph.D., engages in inverse problems and their applications, computation in ¯nance.
Supported by:
Supported by the National Natural Science Foundation of China(11171349)；

摘要/Abstract

摘要： This paper concerns an inverse problem of recovering implied volatility in shortterm interest rate model from the market prices of zero-coupon bonds. Based on linearization, an analytic solution, which is given as a power series, is derived for the direct problem.By neglecting high order terms in the power series, an integral equation about the perturbation of volatility is formulated and the Tikhonov regularization method is applied to solve the integral equation. Finally numerical experiments are given and the results show that the method is effective.

关键词: implied volatility, inverse problem, linearization

Abstract: This paper concerns an inverse problem of recovering implied volatility in shortterm interest rate model from the market prices of zero-coupon bonds. Based on linearization, an analytic solution, which is given as a power series, is derived for the direct problem.By neglecting high order terms in the power series, an integral equation about the perturbation of volatility is formulated and the Tikhonov regularization method is applied to solve the integral equation. Finally numerical experiments are given and the results show that the method is effective.

Key words: implied volatility, inverse problem, linearization

中图分类号:

F830.91

赵芳芳, 许作良. 短期利率模型中隐含波动率的重构[J]. 数学季刊, 2017, 32(4): 395-406.

ZHAO Fang-fang, XU Zuo-liang. Recover Implied Volatility in Short-term Interest Rate Model[J]. Chinese Quarterly Journal of Mathematics, 2017, 32(4): 395-406.

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短期利率模型中隐含波动率的重构

Recover Implied Volatility in Short-term Interest Rate Model

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