Abstract
A parameter estimation method, called PMCMC in this paper, is proposed to estimate a continuous-time model of the term structure of interests under Markov regime switching and jumps. There is a closed form solution to term structure of interest rates under Markov regime. However, the model is extended to be a CKLS model with non-closed form solutions which is a typical nonlinear and non-Gaussian state-space model(SSM) in the case of adding jumps. Although the difficulty of parameter estimation greatly prevents from researching models, we prove that the nonlinear and non-Gaussian state-space model has better performances in studying volatility. The method proposed in this paper will be implemented in simulation and empirical study for SHIBOR. Empirical results illustrate that the PMCMC algorithm has powerful advantages in tackling the models.
Supported by National Natural Science Foundation of China (71471075), Fundamental Research Funds for the Central University (19JNLH09) and Humanities and Social Sciences Foundation of Ministry of Education, China (14YJAZH052)
References
[1] Bolstad W M. Understanding computational Bayesian statistics. New York: Wiley, 2010.10.1002/9780470567371Search in Google Scholar
[2] Chorin A J, Morzfeld M, Tu X M. State-space models applications in economics and finance. Statistics and Econometrics for Finance, Springer, 2013: 63–88.10.1007/978-1-4614-7789-1_3Search in Google Scholar
[3] Crisan D, Doucet A. A survey of convergence results on particle filtering methods for practitioners. IEEE Transactions on Signal Processing, 2002, 50: 736–746.10.1109/78.984773Search in Google Scholar
[4] DelMoral P, Doucet A, Jasra A. On adaptive resampling procedures for sequential Monte Carlo methods. Bernoulli, 2012, 18: 252–278.10.3150/10-BEJ335Search in Google Scholar
[5] Douc R, Moulines E. Limit theorems for weighted samples with applications to sequential Monte Carlo methods. The Annals of Statistics, 2008, 36: 2344–2376.10.1214/07-AOS514Search in Google Scholar
[6] Gordon N J, Salmond D J, Smith A F M. Novel approach to nonlinear/non-Gaussian Bayesian state estimation. Radar and Signal Processing, IEEE Proceedings F, 1993, 140(2): 107–113.10.1049/ip-f-2.1993.0015Search in Google Scholar
[7] Carpenter J, Clifford P, Fearnhead P. An improved particle filter for nonlinear problems. Radar, Sonar and Navigation, IEE Proceedings, 1999, 146: 2–7.10.1049/ip-rsn:19990255Search in Google Scholar
[8] Liu J S, Chen R. Sequential Monte Carlo methods for dynamic systems. Journal of American Statistical Association, 1998, 93: 1032–1044.10.1080/01621459.1998.10473765Search in Google Scholar
[9] Doucet A, Godsill S, Andrieu C. On sequential Monte Carlo sampling methods for Bayesian filtering. Statistics and Computing, 2000, 10: 197–208.10.1023/A:1008935410038Search in Google Scholar
[10] Doucet A, Johansen A M. A tutorial on particle filtering and smoothing: Fifteen years later. Handbook of Nonlinear Filtering, 2011.Search in Google Scholar
[11] Geweke J, Tanizaki H. Bayesian estimation of state-space model using the Metropolis-Hastings algorithm within Gibbs sampling. Computational Statistics & Data Analysis, 2001, 37(2): 151–170.10.1016/S0167-9473(01)00009-3Search in Google Scholar
[12] Lopes H F, Tsay R S. Particle filters and Bayesian inference in financial econometrics. Journal of Forecasting, 2011, 30: 196–209.10.1002/for.1195Search in Google Scholar
[13] Metropolis N, Rosenbluth A W, Rosenbluth M N, et al. Equation of state calculations by fast computing machines. Journal of Chemical Physics, 1953, 21: 1078–1092.10.2172/4390578Search in Google Scholar
[14] Pitt M K, Shephard N. Filtering via simulation: Auxiliary particle filters. Journal of American Statistical Association, 1999, 94(446): 590–599.10.1080/01621459.1999.10474153Search in Google Scholar
[15] Zeng Y, Wu S. State-Space Models applications in economics and finance. Statistics and Econometrics for Finance, Springer, 2013.Search in Google Scholar
[16] Storvik G. Particle filters in state space models with the presence of unknown static parameters. IEEE: Transactions of Signal Processing, 2002, 50: 281–289.10.1109/78.978383Search in Google Scholar
[17] Xiong J, Zeng Y. A branching particle approximation to the filtering problem with counting process observations. Statistical Inference for Stochastic Processes, 2011, 14: 111–140.10.1007/s11203-011-9053-3Search in Google Scholar
[18] Johannes M, Polson N, Stroud J. Optimal filtering of jump diffusions: Extracting latent states from asset prices. Review of Financial Studies, 2009, 22(7): 2559–2599.10.1093/rfs/hhn110Search in Google Scholar
[19] Malik S, Pitt M K. Particle filters for continuous likelihood evaluation and maximisation. Journal of Econometrics, 2011, 165(2): 190–209.10.1016/j.jeconom.2011.07.006Search in Google Scholar
[20] Carvalho C M, Lopes H F. Simulation-based sequential analysis of Markov switching stochastic volatility models. Computational Statistics & Data Analysis, 2007, 51(9): 4526–4542.10.1016/j.csda.2006.07.019Search in Google Scholar
[21] Rios M P, Lopes H F. The extended Liu and west filter: Parameter learning in Markov switching stochastic volatility models. Chapter 2, in this volume, 2013.10.1007/978-1-4614-7789-1_2Search in Google Scholar
[22] Christoffersen P, Jacobs K, Mimouni K. Volatility dynamics for the S&P 500: Evidence from realized volatility, daily returns, and option prices. Review of Financial Studies, 2010, 23: 3141–3189.10.2139/ssrn.1150644Search in Google Scholar
[23] Fernández-Villaverde J, Rubio-Ramírez J F. Estimating macroeconomic models: A Likelihood Approach. Review of Economic Studies, 2007, 74(4): 1059–1087.10.3386/t0321Search in Google Scholar
[24] An S, Schorfheide F. Bayesian analysis of DSGE models. Econometric Reviews, 2007, 26(2–4): 113–172.10.21799/frbp.wp.2006.05Search in Google Scholar
[25] Sarkka S, Solin A, Hartikainan J. Spatiotemporal learning via infinite-dimensional Bayesian filtering and smoothing. IEEE Signal Processing Magazine, 2013, 30(4): 51–61.10.1109/MSP.2013.2246292Search in Google Scholar
[26] Zeng Y. A partially observed model for micromovement of asset prices with Bayes estimation via filtering. Mathematical Finance, 2003, 13: 411–444.10.1111/1467-9965.t01-1-00022Search in Google Scholar
[27] Andrieu C, Doucet A, Holenstein R. Particle Markov chain Monte Carlo methods. Journal of the Royal Statistical Society, 2010, 72: 269–342.10.1111/j.1467-9868.2009.00736.xSearch in Google Scholar
[28] Wu S, Zeng Y. Affine regime-switching models for interest rate term structure. Mathematics of Finance, 2004, 351: 375–386.10.1090/conm/351/06417Search in Google Scholar
[29] Wu S, Zeng Y. A general equilibrium model of the term structure of interest rates under regime-switching risk. International Journal of Theoreticaland Applied Finance, 2005, 8: 839–869.10.1142/S0219024905003323Search in Google Scholar
[30] Wu S, Zeng Y. The term structure of interest rates under regime shifts and jumps. Economics Letters, Elsevier, 2006, 93: 215–221.10.1016/j.econlet.2006.05.006Search in Google Scholar
© 2020 Walter De Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Could the Stock Market Adjust Itself? An Empirical Study Based on Mean Reversion Theory
- Research on the Satisfaction Impact Factors of China-Eurasia Expo: From the Perspectives of Local Residents and Exhibitors
- Study on the Measurement of Industrial Structure “Sophistication, Rationalization and Ecologicalization” Based on the Dynamic Analysis of Grey Relations — A Case Study of Beijing-Tianjin-Hebei
- Can Positive Entrepreneurship Policies Always Improve Social Welfare?
- PMCMC for Term Structure of Interest Rates under Markov Regime Switching and Jumps
- How to Bid Success in Crowdsourcing Contest? ― Evidence from the Translation Tasks of Tripadvisor
- Single Image Dehazing with V-transform and Dark Channel Prior
Articles in the same Issue
- Could the Stock Market Adjust Itself? An Empirical Study Based on Mean Reversion Theory
- Research on the Satisfaction Impact Factors of China-Eurasia Expo: From the Perspectives of Local Residents and Exhibitors
- Study on the Measurement of Industrial Structure “Sophistication, Rationalization and Ecologicalization” Based on the Dynamic Analysis of Grey Relations — A Case Study of Beijing-Tianjin-Hebei
- Can Positive Entrepreneurship Policies Always Improve Social Welfare?
- PMCMC for Term Structure of Interest Rates under Markov Regime Switching and Jumps
- How to Bid Success in Crowdsourcing Contest? ― Evidence from the Translation Tasks of Tripadvisor
- Single Image Dehazing with V-transform and Dark Channel Prior