응용통계연구 (The Korean Journal of Applied Statistics)

  • 제27권6호
  • /
  • Pages.959-973
  • /
  • 2014
  • /
  • 1225-066X(pISSN)
  • /
  • 2383-5818(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지
DOI QR코드

DOI QR Code

비대칭적 점프확산 모형의 효율적인 베이지안 추론

Efficient Bayesian Inference on Asymmetric Jump-Diffusion Models

  • 박태영 (연세대학교 응용통계학과) ;
  • 이영은 (연세대학교 응용통계학과)
  • Park, Taeyoung (Department of Applied Statistics, Yonsei University) ;
  • Lee, Youngeun (Department of Applied Statistics, Yonsei University)
  • 투고 : 2014.10.06
  • 심사 : 2014.10.30
  • 발행 : 2014.12.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

자산가격의 비대칭적 변동을 설명하기 위해 최근 비대칭적 점프확산 모형이 제안되었다. 본 논문에서는 이러한 자산가격 모형을 분석하는데 사용되는 효율적인 베이지안 방법을 제안한다. 본 논문에서 제안되는 방법은 모형 요소가 쉽게 추출되는 편의성을 희생하지 않으면서도 조건부 분포들간의 함수적 비호환성을 통해 효율성을 향상시킬 수 있는 부분붕괴 깁스 샘플러를 고안함으로써 개발되었다. 제안된 방법은 모의실험 자료에 적용되어 그 효율성을 검증하였고 1980년 9월부터 2014년 8월까지 관찰된 일별 S&P 500 자료에 적용되었다.

Asset pricing models that account for asymmetric volatility in asset prices have been recently proposed. This article presents an efficient Bayesian method to analyze asset-pricing models. The method is developed by devising a partially collapsed Gibbs sampler that capitalizes on the functional incompatibility of conditional distributions without complicating the updates of model components. The proposed method is illustrated using simulated data and applied to daily S&P 500 data observed from September 1980 to August 2014.

키워드

참고문헌

  1. Andersen, T. G., Benzoni, L. and Lund, J. (2002). Empirical investigation of continuous-time equity return models, Journal of Finance, 57, 1239-1284. https://doi.org/10.1111/1540-6261.00460
  2. Besag, J. and Green, P. J. (1993). Spatial statistics and Bayesian computation, Journal of the Royal Statistical Society, Series B, 55, 25-37.
  3. Gelfand, A. E., Sahu, S. K. and Carlin, B. P. (1995). Efficient parameterization for normal linear mixed models, Biometrika, 82, 479-488. https://doi.org/10.1093/biomet/82.3.479
  4. Gelman, A. and Rubin, D. B. (1992). Inference from iterative simulations using multiple sequences (with discussion), Statistical Science, 7, 457-472. https://doi.org/10.1214/ss/1177011136
  5. Kou, S. G. (2002). A jump-diffusion model for option pricing, Management Science, 48, 1086-1101. https://doi.org/10.1287/mnsc.48.8.1086.166
  6. Liu, J. S. (1994). The collapsed Gibbs sampler in Bayesian computations with applications to gene regulation problem, Journal of the American Statistical Association, 89, 958-966. https://doi.org/10.1080/01621459.1994.10476829
  7. Liu, J. S., Wong, W. H. and Kong, A. (1994). Covariance structure of the Gibbs sampler with applications to comparisons of estimators and augmentation schemes, Biometrika, 81, 27-40. https://doi.org/10.1093/biomet/81.1.27
  8. Liu, J. S. and Wu, Y. N. (1999). Parameter expansion for data augmentation, Journal of the American Statistical Association, 94, 1264-1274. https://doi.org/10.1080/01621459.1999.10473879
  9. Meng, X. L. and van Dyk, D. A. (1999). Seeking efficient data augmentation schemes via conditional and marginal augmentation, Biometrika, 86, 301-320. https://doi.org/10.1093/biomet/86.2.301
  10. Merton, R. C. (1976). Option pricing when underlying stock returns are discontinuous, Journal of Financial Economics, 3, 125-144. https://doi.org/10.1016/0304-405X(76)90022-2
  11. Park, T. (2009). Statistical challenges in spectral analysis in high-energy astrophysics, ISBA Bulletin, 16, 13-17.
  12. Park, T. (2011). Bayesian analysis of individual choice behavior with aggregate data, Journal of Computational and Graphical Statistics, 20, 158-173. https://doi.org/10.1198/jcgs.2010.10006
  13. Park, T. and Bae, W. (2014). Bayesian semi-parametric regression for quantile residual lifetime, Communications for Statistical Applications and Methods, 21, 285-296. https://doi.org/10.5351/CSAM.2014.21.4.285
  14. Park, T., Jeong, J. and Lee, J. (2012a). Bayesian nonparametric inference on quantile residual life function: Application to breast cancer data, Statistics In Medicine, 31, 1972-1985. https://doi.org/10.1002/sim.5353
  15. Park, T., Krafty, R. T. and Sanchez, A. I. (2012b). Bayesian semi-parametric analysis of Poisson change-point regression models: Application to policy making in Cali, Colombia, Journal of Applied Statistics, 39, 2285-2298. https://doi.org/10.1080/02664763.2012.709227
  16. Park, T. and Min, S. (2014). Partially collapsed Gibbs sampling for linear mixed-effects models, Communications in Statistics - Simulation and Computation, DOI:10.1080/03610918.2013.857687.
  17. Park, T. and van Dyk, D. A. (2009). Partially collapsed Gibbs samplers: Illustrations and applications, Journal of Computational and Graphical Statistics, 18, 283-305. https://doi.org/10.1198/jcgs.2009.08108
  18. Park, T., van Dyk, D. A. and Siemiginowska, A. (2008). Searching for narrow emission lines in X-ray spectra: Computation and methods, The Astrophysical Journal, 688, 807-825. https://doi.org/10.1086/591631
  19. Ramezani, C. A. and Zeng, Y. (1998). Maximum likelihood estimation of asymmetric jump-diffusion process: Cpplication to security prices, Working Paper, Department of Mathematics and Statistics, University of Missouri, Kansas City, Available from: http://ssrn.com/abstract=606361.
  20. Ramezani, C. A. and Zeng, Y. (2007). Maximum likelihood estimation of the double exponential jump diffusion process, Annals of Finance, 3, 487-507. https://doi.org/10.1007/s10436-006-0062-y
  21. Roberts, G. O., Gelman, A. and Gilks, W. (1997). Weak convergence and optimal scaling of random walk Metropolis algorithms, The Annals of Applied Probability, 7, 110-120. https://doi.org/10.1214/aoap/1034625254
  22. Roberts, G. O. and Rosenthal, J. S. (2001). Optimal scaling for various Metropolis-Hastings algorithms, Statistical Science, 16, 351-367. https://doi.org/10.1214/ss/1015346320
  23. Roberts, G. O. and Rosenthal, J. S. (2007). Coupling and ergodicity of adaptive MCMC, Journal of Applied Probability, 44, 458-475. https://doi.org/10.1239/jap/1183667414
  24. van Dyk, D. A. (2000). Nesting EM algorithms for computational efficiency, Statistical Sinica, 10, 203-225.
  25. van Dyk, D. A. and Park, T. (2008). Partially collapsed Gibbs samplers: Theory and methods, Journal of the American Statistical Association, 193, 790-796.
  26. van Dyk, D. A. and Park, T. (2011). Partially collapsed Gibbs sampling and path-adaptive Metropolis-Hastings in high-energy astrophysics, Handbook of Markov Chain Monte Carlo, Chapman & Hall/CRC Press, 383-400.
  27. Xu, X., Meng, X. L., and Yu, Y. (2013). Thank God that regressing Y on X is not the same as regressing X on Y: Direct and indirect residual augmentations, Journal of Computational and Graphical Statistics, 22, 598-622. https://doi.org/10.1080/10618600.2013.794702
  28. Yu, Y. and Meng, X. L. (2011). To center or not to center, that is not the question: An ancillarity-sufficiency interweaving strategy(ASIS) for boosting MCMC efficiency, Journal of Computational and Graphical Statistics, 20, 531-570. https://doi.org/10.1198/jcgs.2011.203main

피인용 문헌

  1. Bayesian inference on multivariate asymmetric jump-diffusion models vol.29, pp.1, 2016, https://doi.org/10.5351/KJAS.2016.29.1.099