短期利率模型中隐含波动率的重构

赵芳芳, 许作良

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

数学季刊 >

2017 , Vol. 32 >Issue 4: 395 - 406

DOI: https://doi.org/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

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

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.

收稿日期: 2015-07-07

网络出版日期: 2020-10-20

基金资助

Supported by the National Natural Science Foundation of China(11171349)；

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Recover Implied Volatility in Short-term Interest Rate Model

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

Received date: 2015-07-07

Online published: 2020-10-20

Supported by

Supported by the National Natural Science Foundation of China(11171349)；

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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

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

Abstract

Key words： implied volatility; inverse problem; linearization

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