Bayesian inference on multivariate asymmetric jump-diffusion models

다변량 비대칭 라플라스 점프확산 모형의 베이지안 추론

Lee, Youngeun;Park, Taeyoung

  • Received : 2015.12.14
  • Accepted : 2015.12.23
  • Published : 2016.02.29


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.


Bayesian analysis;collapsed Gibbs sampler;data augmentation;Markov Chain Monte Carlo;multivariate asymmetric Laplace distribution


  1. Black, F. and Scholes, M. (1973). The pricing of options and corporate liabilities, The Journal of Political Economy, 637-654.
  2. Duffie, D. and Pan, J. (2001). Analytical value-at-risk with jumps and credit risk, Finance and Stochastics, 5, 155-180.
  3. Frame, S. J. and Ramezani, C. A. (2014). Bayesian estimation of asymmetric jump-diffusion processes, Annals of Financial Economics, 9, 1450008.
  4. Gelman, A. and Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences, Statistical Science, 467-472.
  5. Heston, S. L. (1993). A closed-form solution for options with stochastic volatility with applications to bond and currency options, Review of Financial Studies, 6, 327-343
  6. Huang, Z. and Kou, S. G. (2006). First passage times and analytical solutions for options on two assets with jump risk, Columbia University.
  7. Hull, J. and White, A. (1987). The pricing of options on assets with stochastic volatilities, The Journal of Finance, 42, 281-300
  8. Jacquier, E., Johannes, M., and Polson, N. (2007). MCMC maximum likelihood for latent state models, Journal of Econometrics, 137, 615-640.
  9. Johannes, M. and Polson, N. (2002). MCMC methods for financial econometrics, The Handbook of Financial Econometrics, 65.
  10. Kotz, S., Kozubowski, T., and Podgorski, K. (2012). The Laplace Distribution and Generalizations: A Revisit with Applications to Communications, Economics, Engineering, and Finance, Springer Science & Business Media, New York.
  11. Kou, S. G. (2002). A jump-diffusion model for option pricing, Management Science, 48, 1086-1101.
  12. Kou, S. G. (2007). Jump-diffusion models for asset pricing in financial engineering, Handbooks in Operations Research and Management Science, 15, 73-116
  13. 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.
  14. 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, Biometricka, 81, 27-40.
  15. Liu, J. S. and Wu, Y. N. (1999). Parameter expansion for data augmentation, Journal of the American Statistical Association, 94, 1264-1274.
  16. Meng, X.-L. and van Dyk, D. A. (1999). Seeking efficient data augmentation schemes via conditional and marginal augmentation, Biometrika, 86, 301-320.
  17. Merton, R. C. (1976). Option pricing when underlying stock returns are discontinuous, Journal of Financial Economics, 3, 125-144.
  18. Park, T. and Lee, Y. (2014). Efficient Bayesian inference on asymmetric jump-diffusion models, Korean Journal of Applied Statistics, 27, 959-973
  19. Park, T. and Min, S. (2016). Partially collapsed Gibbs sampling for linear mixed-effects models, Communi- cations in Statistics - Simulation and Computation, 45, 165-180
  20. Park, T. and van Dyk, D. A. (2009). Partially collapsed Gibbs samplers: Illustrations and applications, Journal of Computational and Graphical Statistics, 18, 283-305.
  21. Ramezani, C. A. and Zeng, Y. (1998). Maximum likelihood estimation of asymmetric jump-diffusion process: Application to security prices, Working Paper, Department of Mathematics and Statistics, University of Missouri, Kansas City, Available from:
  22. Ramezani, C. A. and Zeng, Y. (2007). Maximum likelihood estimation of the double exponential jump diffusion process, Annals of Finance, 3, 487-507.
  23. Tanner, M. A. and Wong, W. H. (1987). The calculation of posterior distributions by data augmentation, Journal of the American Statistical Association, 82, 528-540.
  24. van Dyk, D. A. and Park, T. (2008). Partially collapsed Gibbs samplers: theory and methods, Journal of the American Statistical Association, 193, 790-796.
  25. van Dyk, D. A. (2000). Nesting EM algorithms for computational efficiency, Statistical Sinica, 10, 203-225.
  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 (383-400), Chapman & Hall/CRCPress, New York.


Supported by : 한국연구재단