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

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)1066-1079
Number of pages14
JournalInternational Journal of Computer Mathematics
Volume99
Issue number5
DOIs
Publication statusPublished - 2022

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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