Reconstructing the Local Volatility Surface from Market Option Prices

Soobin Kwak, Youngjin Hwang, Yongho Choi, Jian Wang, Sangkwon Kim, Junseok Kim

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

We present an efficient and accurate computational algorithm for reconstructing a local volatility surface from given market option prices. The local volatility surface is dependent on the values of both the time and underlying asset. We use the generalized Black–Scholes (BS) equation and finite difference method (FDM) to numerically solve the generalized BS equation. We reconstruct the local volatility function, which provides the best fit between the theoretical and market option prices by minimizing a cost function that is a quadratic representation of the difference between the two option prices. This is an inverse problem in which we want to calculate a local volatility function consistent with the observed market prices. To achieve robust computation, we place the sample points of the unknown volatility function in the middle of the expiration dates. We perform various numerical experiments to confirm the simplicity, robustness, and accuracy of the proposed method in reconstructing the local volatility function.

Original languageEnglish
Article number2537
JournalMathematics
Volume10
Issue number14
DOIs
Publication statusPublished - 2022 Jul

Bibliographical 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.

Publisher Copyright:
© 2022 by the authors.

Keywords

  • Black–Scholes equations
  • finite difference method
  • local volatility function
  • option pricing

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • General Mathematics
  • Engineering (miscellaneous)

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