Journal for History of Mathematics (한국수학사학회지)

The Korean Society for History of Mathematics (한국수학사학회)
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Gaussian Process Regression and Its Application to Mathematical Finance

가우시언 과정의 회귀분석과 금융수학의 응용

  • Received : 2022.01.21
  • Accepted : 2022.02.13
  • Published : 2022.02.28
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Abstract

This paper presents a statistical machine learning method that generates the implied volatility surface under the rareness of the market data. We apply the practitioner's Black-Scholes model and Gaussian process regression method to construct a Bayesian inference system with observed volatilities as a prior information and estimate the posterior distribution of the unobserved volatilities. The variance instead of the volatility is the target of the estimation, and the radial basis function is applied to the mean and kernel function of the Gaussian process regression. We present two types of Gaussian process regression methods and empirically analyze them.

Keywords

Acknowledgement

Lim supported by NRF-2019R1I1A3A03059382, and BK21 FOUR (Fostering Outstanding Universities for Research, NO.5120200913674) funded by the Ministry of Education(MOE, Korea) and NRF, 이 논문은 전남대학교 학술연구비(과제번호: 2021-2529) 지원에 의하여 연구되었음.

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