한국수학사학회지 (Journal for History of Mathematics)

한국수학사학회 (The Korean Society for History of Mathematics)
권호 표지
DOI QR코드

DOI QR Code

가우시언 과정의 회귀분석과 금융수학의 응용

Gaussian Process Regression and Its Application to Mathematical Finance

  • 투고 : 2022.01.21
  • 심사 : 2022.02.13
  • 발행 : 2022.02.28
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

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.

키워드

과제정보

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.

참고문헌

  1. T. W. Anderson, An Introduction to Multivariate Statistical Analysis, John Wiley & Sons, 2003.
  2. F. Black, The Pricing of Commodity Contracts, Journal of Financial Economics, 3 (1976), 167-179. https://doi.org/10.1016/0304-405X(76)90024-6
  3. F. Black, Myron Schoels, The Pricing of Options and Corporate Liabilities, Journal of Polytical Economy 81(3) (1973), 637-654. https://doi.org/10.1086/260062
  4. Bernard Dumas, Jeff Fleming and Robert E. Whaley, Implied volatility functions: Empirical tests, The Journal of Finance, LIII0 (6): 2059-2106, 1998.
  5. Gregory E. Fasshauer, Meshfree approximation methods with MATLAB, World Scientific, 2007.
  6. Lim Hyuncheul, Construction of the Implied Volatility Surface by Thin Plate Spline Function, 금융공학연구 18(4) (2019), 1-36.
  7. Bertil Matern, Wiley StatsRef: Statistics Reference Online 2018.
  8. Jorge Nocedal, Numerical Optimization, Volume 2, 2nd Edition, volume 1, Springer, 1999.
  9. Carl E. Rasmussen and Christopher K. I. Williams, Gaussian processes for machine learning, MIT press, Cambridge, MA, 2006.
  10. Grace Wahba, Spline models for observational data, Siam, 1990.