Calibration of the temporally varying volatility and interest rate functions

Eunchae Park; Jisang Lyu; Sangkwon Kim; Chaeyoung Lee; Wonjin Lee; Yongho Choi; Soobin Kwak; Changwoo Yoo; Hyeongseok Hwang; Junseok Kim

doi:10.1080/00207160.2021.1948539

Calibration of the temporally varying volatility and interest rate functions

Eunchae Park, Jisang Lyu, Sangkwon Kim, Chaeyoung Lee, Wonjin Lee, Yongho Choi, Soobin Kwak, Changwoo Yoo, Hyeongseok Hwang, Junseok Kim

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this study, we develop a calibration method of the temporally varying volatility and interest rate functions using the Black–Scholes (BS) partial differential equation and the observed market option prices with different strikes and expiries. The proposed method uses the piecewise linear interpolations between data points which are defined at the middle points of maturity dates. When we construct the volatility and interest rate, we use the exponential function so that the interpolated values are always positive. Numerical experiments with synthetic and real market data demonstrate the superior performance of the proposed method.

Original language	English
Journal	International Journal of Computer Mathematics
DOIs	https://doi.org/10.1080/00207160.2021.1948539
Publication status	Accepted/In press - 2021

Keywords

Black–Scholes equation
calibration
interest rate
option price
volatility

ASJC Scopus subject areas

Computer Science Applications
Computational Theory and Mathematics
Applied Mathematics

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10.1080/00207160.2021.1948539

Cite this

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title = "Calibration of the temporally varying volatility and interest rate functions",

abstract = "In this study, we develop a calibration method of the temporally varying volatility and interest rate functions using the Black–Scholes (BS) partial differential equation and the observed market option prices with different strikes and expiries. The proposed method uses the piecewise linear interpolations between data points which are defined at the middle points of maturity dates. When we construct the volatility and interest rate, we use the exponential function so that the interpolated values are always positive. Numerical experiments with synthetic and real market data demonstrate the superior performance of the proposed method.",

keywords = "Black–Scholes equation, calibration, interest rate, option price, volatility",

author = "Eunchae Park and Jisang Lyu and Sangkwon Kim and Chaeyoung Lee and Wonjin Lee and Yongho Choi and Soobin Kwak and Changwoo Yoo and Hyeongseok Hwang and Junseok Kim",

note = "Funding Information: The corresponding author (J.S. Kim) was supported by the Brain Korea 21 FOUR through the National Research Foundation of Korea funded by the Ministry of Education of Korea. The authors thank the reviewers for their constructive and helpful comments on the revision of this article. Publisher Copyright: {\textcopyright} 2021 Informa UK Limited, trading as Taylor & Francis Group.",

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doi = "10.1080/00207160.2021.1948539",

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AU - Park, Eunchae

AU - Lyu, Jisang

AU - Kim, Sangkwon

AU - Lee, Chaeyoung

AU - Lee, Wonjin

AU - Choi, Yongho

AU - Kwak, Soobin

AU - Yoo, Changwoo

AU - Hwang, Hyeongseok

AU - Kim, Junseok

N1 - Funding Information: The corresponding author (J.S. Kim) was supported by the Brain Korea 21 FOUR through the National Research Foundation of Korea funded by the Ministry of Education of Korea. The authors thank the reviewers for their constructive and helpful comments on the revision of this article. Publisher Copyright: © 2021 Informa UK Limited, trading as Taylor & Francis Group.

PY - 2021

Y1 - 2021

N2 - In this study, we develop a calibration method of the temporally varying volatility and interest rate functions using the Black–Scholes (BS) partial differential equation and the observed market option prices with different strikes and expiries. The proposed method uses the piecewise linear interpolations between data points which are defined at the middle points of maturity dates. When we construct the volatility and interest rate, we use the exponential function so that the interpolated values are always positive. Numerical experiments with synthetic and real market data demonstrate the superior performance of the proposed method.

AB - In this study, we develop a calibration method of the temporally varying volatility and interest rate functions using the Black–Scholes (BS) partial differential equation and the observed market option prices with different strikes and expiries. The proposed method uses the piecewise linear interpolations between data points which are defined at the middle points of maturity dates. When we construct the volatility and interest rate, we use the exponential function so that the interpolated values are always positive. Numerical experiments with synthetic and real market data demonstrate the superior performance of the proposed method.

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KW - calibration

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JO - International Journal of Computer Mathematics

JF - International Journal of Computer Mathematics

SN - 0020-7160

ER -

Calibration of the temporally varying volatility and interest rate functions

Abstract

Keywords

ASJC Scopus subject areas

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