Author(s)

JingShu Liu

Affiliation(s)

Questrom School of Business, Boston University, Boston 02215, MA, US.

Corresponding Author

JingShu Liu

ABSTRACT

This paper develops a Bayesian Markov Chain Monte Carlo (MCMC) estimation method for multi-factor affine term structure models (ATSMs). ATSMs are popular, but efficient estimation methods for them are not readily available. Using simulated price data, the MCMC algorithms developed provide good estimates with their posterior distributions converge. With real historical data, the in-sample pricing errors obtained are significantly smaller than those obtained from alternative methods. A Bayesian forecast analysis documents the superior predictive power of the MCMC approach. Finally, Bayesian model selection criteria are discussed.

KEYWORDS

Affine term structure model; Markov Chain Monte Carlo; Interest rate modeling

CITE THIS PAPER

JingShu Liu. Affine term structure model with MCMC. Journal of Trends in Financial and Economics. 2024, 1(1): 62-75. DOI: 10.61784/jtfe3012.

REFERENCES

[1] Q Dai, KJ Singleton. Specification analysis of affine term structure models. Journal of Finance, 2000, 55(5): 1943–1978.

[2] GR Duffee. Term premia and interest rate forecasts in affine models. Journal of Finance, 2002, 57(1): 405–443, .

[3] P Cheridito, D Filipovic, RL Kimmel. Market price of risk specifications for affine models: Theory and evidence. Journal of Financial Economics, 2007, 83(1): 123–170.

[4] Y Ait-Sahalia, RL Kimmel. Estimating affine multi factor term structure model using closed-form likelihood expansions. Journal of Financial Economics, 2010, 98(1): 113–144.

[5] JD Hamilton, JC Wu. Identification and estimation of Gaussian affine term structure models. Journal of Econometrics, 2012, 168(2): 315–331.

[6] M Piazzesi. Affine term structure models. In Handbook of Financial Econometrics. Elsevier, 2008.

[7] AR Pedersen. A new approach to maximum likelihood estimation for stochastic differential equations based on discrete observations. Scandinavian Journal of Statistics, 1995, 22(1): 55–71.

[8] MW Brandt, P Santa-Clara. Simulated likelihood estimation of diffusions with an application to exchange rate dynamics in incomplete markets. Journal of Financial Economics, 2002, 63(2): 161–210.

[9] RR Chen, L Scott. Multi-factor Cox-Ingersoll-Ross models of the term structure: Estimates and tests from a Kalman filter model. Journal of Fixed Income, 1993, 3 (3): 14–31.

[10] P Collin-Dufresne, RS Goldstein, CS Jones. Identification of maximal affine term structure models. Journal of Finance, 2008, 63(2)743–795.

[11] Nelson-Siegel term structure models. Journal of Econometrics, 2011, 164(1): 4–20.

[12] LEO Svensson. Estimating and interpreting forward interest rates: Sweden 1992-1994. NBER Working Papers 4871, National Bureau of Economic Research, Inc., 1994.

[13] CM Bishop. Pattern Recognition and Machine Learning (Information Science and Statistics). Springer, 2nd edition, 2007.

[14] E Jacquier, NG Polson, PE Rossi. Bayesian analysis of stochastic volatility models. Journal of Business and Economic Statistics, 1994, 12(4): 371–389.

[15] E Jacquier, NG Polson, PE Rossi. Bayesian analysis of stochastic volatility models with fat-tails and correlated errors. Journal of Econometrics, 2004, 122(1): 185– 212.

[16] B Eraker, M Johannes, N Polson. The impact of jumps in volatility and returns. Journal of Finance, 2003, 58(3): 1269–1300.

[17] M Johannes, N Polson. MCMC methods for continuous-time financial econometrics. In Handbook of Financial Econometrics. Elsevier, 2007.

[18] H Hu. Markov chain Monte Carlo estimation of multi-factor affine term-structure models. Unpublished doctoral dissertation, University of California, Los Angeles, 2005.

[19] CP Robert, G Casella. Monte Carlo Statistical Methods. Springer, 2nd edition, 2004.

[20] S Geman, D Geman. Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Ma- chine Intelligence, 1984, 6(6): 721–741.

[21] JM Hammersley, PE Clifford. Markov random fields on finite graphs and lattices. Unpublished manuscript, 1971.

[22] CK Carter, R Kohn. On Gibbs sampling for state space models. Biometrika, 1994, 81(3): 541–553.

[23] S Fruwirth-Schnatter. Data augmentation and dynamic linear models. Journal of Time Series Analysis, 1994, 15(2): 183–202.

[24] RE Kalman. A new approach to linear filtering and prediction problems. Transactions of the ASME-Journal of Basic Engineering, 1960, 82(1): 35–45.

[25] RE Kass, AE Raftery. Bayes factors. Journal of the American Statistical Association, 1995, 90(430): 773–795.

[26] L Tierney, JB Kadane. Accurate approximations for posterior moments and marginal densities. Journal of the American Statistical Association, 1986, 81(393): 82–86.

[27] MA Newton, AE Raftery. Approximate Bayesian inference with the weighted likelihood bootstrap. Journal of the Royal Statistical Society. Series B (Methodological), 1994, 56(1): 3–48.

[28] D Duffie, J Pan, KJ Singleton. Transform analysis and asset pricing for affine jump-diffusions. Econometrica, 2000, 68(6): 1343–1376.

[29] N Shephard, S Kim. Bayesian analysis of stochastic volatility models: Comment. Journal of Business and Economic Statistics, 1994, 12(4): 406–410.

[30] JHE Christensen, FX Diebold, GD Rudebusch. The affine arbitrage-free class of C.R. Nelson and A.F. Siegel. Parsimonious modeling of yield curves. Journal of Business, 1987, 60(4): 473–489.

[31] CP Robert, G Casella. Introducing Monte Carlo Methods with R. Springer Verlag, 2009.

[32] D Duffie, R Kan. A yield-factor model of interest rates. Mathematical Finance, 1996, 6(4): 379–406.