The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Bayesian inference on multivariate asymmetric jump-diffusion models

다변량 비대칭 라플라스 점프확산 모형의 베이지안 추론

  • Lee, Youngeun (Department of Applied Statistics, Yonsei University) ;
  • Park, Taeyoung (Department of Applied Statistics, Yonsei University)
  • 이영은 (연세대학교 응용통계학과) ;
  • 박태영 (연세대학교 응용통계학과)
  • Received : 2015.12.14
  • Accepted : 2015.12.23
  • Published : 2016.02.29
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Abstract

Asymmetric jump-diffusion models are effectively used to model the dynamic behavior of asset prices with abrupt asymmetric upward and downward changes. However, the estimation of their extension to the multivariate asymmetric jump-diffusion model has been hampered by the analytically intractable likelihood function. This article confronts the problem using a data augmentation method and proposes a new Bayesian method for a multivariate asymmetric Laplace jump-diffusion model. Unlike the previous models, the proposed model is rich enough to incorporate all possible correlated jumps as well as mention individual and common jumps. The proposed model and methodology are illustrated with a simulation study and applied to daily returns for the KOSPI, S&P500, and Nikkei225 indices data from January 2005 to September 2015.

비대칭 점프확산 모형은 자산 가격의 비대칭적 변동을 효과적으로 설명하는 모형으로 활용되어 왔다. 그러나 다변량 모형으로 확장한 다변량 비대칭 라플라스 점프확산 모형은 가능도함수가 닫힌 해로 존재하지 않아 모형의 추론에 한계가 존재하였다. 본 논문에서는 이러한 한계점을 극복하기 위해 자료 확장 기법을 제안하고 새로운 베이지안 추론 방법을 개발한다. 본 논문에서 제안된 모형은 단일 점프와 공통 점프 뿐만 아니라 모든 가능한 조합으로 발생하는 점프를 반영한 확장된 다변량 비대칭 라플라스 점프확산 모형이다. 이러한 모형을 분석하기 위해 붕괴된 깁스 샘플러를 고안한 베이지안 방법을 개발하였다. 본 논문에서 제안된 모형과 방법을 모의실험 자료 및 2005년 1월 3일부터 2015년 9월 30일까지 관찰된 일별 KOSPI, S&P500, 그리고 Nikkei225에 적용하여 효율성을 검증하였다.

Keywords

Acknowledgement

Supported by : 한국연구재단

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