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Arbitrage in the Term Structure of Interest Rates: a Bayesian Approach

Year 2014, Volume: 6 Issue: 2, 77 - 99, 01.09.2014

Márcio Poletti Laurini Armênio Dias Westin Neto

https://doi.org/10.33818/ier.278036

Abstract

This work presents an analysis of the presence of arbitrage opportunities in the term structure of interest rates, through the estimation of the affine generalized Nelson-Siegel model with correction for no-arbitrage. We challenge the necessity of the condition of no-arbitrage using the Brazilian term structure of interest rates by observing the interbank deposits (DI) contracts traded in the Mercantile and Futures Exchange (BM&FBOVESPA) in Brazil between 2007 and 2009. To verify the necessity of imposing no-arbitrage restrictions, we propose an analysis using Bayesian methods of estimation and testing of this model. We also discuss the estimation procedure in the presence of an irregular maturity structure. Our chosen methodology is especially relevant for emerging markets, where the liquidity of emerging markets varies substantially over time, especially in periods of crises. The results of our analysis indicate that the no-arbitrage corrections are not necessary and that this model is an appropriate specification for this term structure of interest rates.

Keywords

Arbitrage term structure of interest rates latent factors Bayesian Inference Nelson-Siegel dynamic models.

References

  • Almeida, C. and J. Vicente (2008). The role of no-arbitrage on forecasting: Lessons from a parametric term structure model. Journal of Banking & Finance, 32 (12), 2695-2705.
  • Ang, A. and M. Piazzesi (2003). A no-arbitrage vector autoregression of term structure dynamics with macroeconomic and latent variables. Journal of Monetary Economics, 50, 745-787.
  • Christensen, J.H.E., F.X. Diebold and G.D. Rudebusch (2011). The Affine Arbitrage-Free Class of Nelson-Siegel Term Structure Models. Journal of Econometrics, 164, 4-20.
  • Christensen, J.H.E., F.X. Diebold and G.D. Rudebush (2009). An Arbitrage-Free Generalized Nelson-Siegel Term Structure Model. Econometrics Journal, 12, 33-64.
  • Cox, J.C., J.E. Ingersoll and S.A. Ross (1985). A theory of the term structure of interest rates. Econometrica, 53, 385–408.
  • Dai, Q. and K. Singleton (2000). Specification analysis of affine term structure models. Journal of Finance, 55, 1943–1978.
  • Delbaen, F. and W. Schachermayer (1994). A general version of the fundamental theory of asset pricing. Mathematische Annalen, 300, 463–250.
  • Diebold, F.X. and C. Li (2006). Forecasting the term structure of government Bond yields. Journal of Econometrics, 130 (2), 337-364.
  • Diebold, F.X. and G.D. Rudebusch (2013). Yield Curve Modeling and Forecasting. Princeton University Press.
  • Duffee, G. (2002). Term premia and interest rate forecasts in affine models. Journal of Finance, 57, 405–443.
  • Duffee, G. (2011). Forecasting with the term structure: The role of no-arbitrage. Working Paper, Johns Hopkins University.
  • Duffie, D. and R. Kan (1996). A yield-factor model of interest rates. Mathematical Finance, 6, 379–406.
  • Filipovic, D. (1999). A note on the Nelson-Siegel family. Mathematical Finance, 9 (4), 349– 359.
  • Gamerman, D. and H. Lopes (2005). Markov Chain Monte Carlo – Stochastic Simulation for Bayesian Inference. CRC Press.
  • Harrison, J. M. and D. Kreps (1979). Martingales and arbitrage in multiperiod securities markets. Journal of Economic Theory, 20, 381–408.
  • Harrison, J. M. and S. Pliska (1981). Martingales and stochastic integrals in the theory of continuous trading. Stochastic Processes and Their Applications, 11, 215–260.
  • Hautsch, N. and F. Yang (2012). Bayesian Inference in Stochastic Volatility Nelson-Siegel Model. Computational Statistics and Data Analysis, 56, 3774–3792.
  • Jeffreys, H. (1961). The Theory of Probability. (3e), Oxford.
  • Joslin, S., K.J. Singleton and H. Zhu (2011). A New Perspective on Gaussian Dynamic Term Structure Models. Review of Financial Studies, 24, 926–970.
  • Laurini, M.P. and L.K. Hotta (2010). Bayesian Extensions to Diebold-Li Term Structure Model. International Review of Financial Analysis, 19, 342-350.
  • Laurini, M.P. and L.K. Hotta (2014). Forecasting the Term Structure of Interest Rates Using Integrated Nested Laplace Approximations. Journal of Forecasting, 33, 214–230.
  • Laurini, M.P. and M. Moura (2010). Constrained smoothing B-splines for the term structure of interest rates. Insurance: Mathematics and Economics, 46, 339–350.
  • Litterman, R. and J. Scheinkman (1991) Common Factors Affecting Bond Returns. Journal of Fixed Income, 1, 54-61.
  • Nelson, C.R. and A.F. Siegel (1987). Parsimonious modeling of yield curves. Journal of Business, 60 (4), 437-489.
  • Raftery, A.E., A.M. Newton, J.M. Satagopan and P.N. Krivitsky (2007). Estimating the Integrated Likelihood via Posterior Simulation Using the Harmonic Mean Identity. Bayesian Statistics, 8, 1–45.
  • Robert, C.P. and G. Casella (2005). Monte Carlo Statistical Methods. Springer.
  • Svensson, L.E. (1994). Estimating and Interpreting Forward Interest Rates: Sweden 1992- 1994. IMF Working Paper, 94.114.
  • Vasicek, O. (1977). An equilibrium characterization of the term structure. Journal of Financial Economics, 5, 177–88.

Year 2014, Volume: 6 Issue: 2, 77 - 99, 01.09.2014

Márcio Poletti Laurini Armênio Dias Westin Neto

https://doi.org/10.33818/ier.278036

Abstract

References

  • Almeida, C. and J. Vicente (2008). The role of no-arbitrage on forecasting: Lessons from a parametric term structure model. Journal of Banking & Finance, 32 (12), 2695-2705.
  • Ang, A. and M. Piazzesi (2003). A no-arbitrage vector autoregression of term structure dynamics with macroeconomic and latent variables. Journal of Monetary Economics, 50, 745-787.
  • Christensen, J.H.E., F.X. Diebold and G.D. Rudebusch (2011). The Affine Arbitrage-Free Class of Nelson-Siegel Term Structure Models. Journal of Econometrics, 164, 4-20.
  • Christensen, J.H.E., F.X. Diebold and G.D. Rudebush (2009). An Arbitrage-Free Generalized Nelson-Siegel Term Structure Model. Econometrics Journal, 12, 33-64.
  • Cox, J.C., J.E. Ingersoll and S.A. Ross (1985). A theory of the term structure of interest rates. Econometrica, 53, 385–408.
  • Dai, Q. and K. Singleton (2000). Specification analysis of affine term structure models. Journal of Finance, 55, 1943–1978.
  • Delbaen, F. and W. Schachermayer (1994). A general version of the fundamental theory of asset pricing. Mathematische Annalen, 300, 463–250.
  • Diebold, F.X. and C. Li (2006). Forecasting the term structure of government Bond yields. Journal of Econometrics, 130 (2), 337-364.
  • Diebold, F.X. and G.D. Rudebusch (2013). Yield Curve Modeling and Forecasting. Princeton University Press.
  • Duffee, G. (2002). Term premia and interest rate forecasts in affine models. Journal of Finance, 57, 405–443.
  • Duffee, G. (2011). Forecasting with the term structure: The role of no-arbitrage. Working Paper, Johns Hopkins University.
  • Duffie, D. and R. Kan (1996). A yield-factor model of interest rates. Mathematical Finance, 6, 379–406.
  • Filipovic, D. (1999). A note on the Nelson-Siegel family. Mathematical Finance, 9 (4), 349– 359.
  • Gamerman, D. and H. Lopes (2005). Markov Chain Monte Carlo – Stochastic Simulation for Bayesian Inference. CRC Press.
  • Harrison, J. M. and D. Kreps (1979). Martingales and arbitrage in multiperiod securities markets. Journal of Economic Theory, 20, 381–408.
  • Harrison, J. M. and S. Pliska (1981). Martingales and stochastic integrals in the theory of continuous trading. Stochastic Processes and Their Applications, 11, 215–260.
  • Hautsch, N. and F. Yang (2012). Bayesian Inference in Stochastic Volatility Nelson-Siegel Model. Computational Statistics and Data Analysis, 56, 3774–3792.
  • Jeffreys, H. (1961). The Theory of Probability. (3e), Oxford.
  • Joslin, S., K.J. Singleton and H. Zhu (2011). A New Perspective on Gaussian Dynamic Term Structure Models. Review of Financial Studies, 24, 926–970.
  • Laurini, M.P. and L.K. Hotta (2010). Bayesian Extensions to Diebold-Li Term Structure Model. International Review of Financial Analysis, 19, 342-350.
  • Laurini, M.P. and L.K. Hotta (2014). Forecasting the Term Structure of Interest Rates Using Integrated Nested Laplace Approximations. Journal of Forecasting, 33, 214–230.
  • Laurini, M.P. and M. Moura (2010). Constrained smoothing B-splines for the term structure of interest rates. Insurance: Mathematics and Economics, 46, 339–350.
  • Litterman, R. and J. Scheinkman (1991) Common Factors Affecting Bond Returns. Journal of Fixed Income, 1, 54-61.
  • Nelson, C.R. and A.F. Siegel (1987). Parsimonious modeling of yield curves. Journal of Business, 60 (4), 437-489.
  • Raftery, A.E., A.M. Newton, J.M. Satagopan and P.N. Krivitsky (2007). Estimating the Integrated Likelihood via Posterior Simulation Using the Harmonic Mean Identity. Bayesian Statistics, 8, 1–45.
  • Robert, C.P. and G. Casella (2005). Monte Carlo Statistical Methods. Springer.
  • Svensson, L.E. (1994). Estimating and Interpreting Forward Interest Rates: Sweden 1992- 1994. IMF Working Paper, 94.114.
  • Vasicek, O. (1977). An equilibrium characterization of the term structure. Journal of Financial Economics, 5, 177–88.
There are 28 citations in total.

Details

Subjects Business Administration
Other ID JA48UT39GM
Journal Section Articles
Authors

Márcio Poletti Laurini This is me

Armênio Dias Westin Neto This is me

Publication Date September 1, 2014
Submission Date September 1, 2014
Published in Issue Year 2014 Volume: 6 Issue: 2

Cite

APA Laurini, M. P., & Neto, A. D. W. (2014). Arbitrage in the Term Structure of Interest Rates: a Bayesian Approach. International Econometric Review, 6(2), 77-99. https://doi.org/10.33818/ier.278036
AMA Laurini MP, Neto ADW. Arbitrage in the Term Structure of Interest Rates: a Bayesian Approach. IER. December 2014;6(2):77-99. doi:10.33818/ier.278036
Chicago Laurini, Márcio Poletti, and Armênio Dias Westin Neto. “Arbitrage in the Term Structure of Interest Rates: A Bayesian Approach”. International Econometric Review 6, no. 2 (December 2014): 77-99. https://doi.org/10.33818/ier.278036.
EndNote Laurini MP, Neto ADW (December 1, 2014) Arbitrage in the Term Structure of Interest Rates: a Bayesian Approach. International Econometric Review 6 2 77–99.
IEEE M. P. Laurini and A. D. W. Neto, “Arbitrage in the Term Structure of Interest Rates: a Bayesian Approach”, IER, vol. 6, no. 2, pp. 77–99, 2014, doi: 10.33818/ier.278036.
ISNAD Laurini, Márcio Poletti - Neto, Armênio Dias Westin. “Arbitrage in the Term Structure of Interest Rates: A Bayesian Approach”. International Econometric Review 6/2 (December 2014), 77-99. https://doi.org/10.33818/ier.278036.
JAMA Laurini MP, Neto ADW. Arbitrage in the Term Structure of Interest Rates: a Bayesian Approach. IER. 2014;6:77–99.
MLA Laurini, Márcio Poletti and Armênio Dias Westin Neto. “Arbitrage in the Term Structure of Interest Rates: A Bayesian Approach”. International Econometric Review, vol. 6, no. 2, 2014, pp. 77-99, doi:10.33818/ier.278036.
Vancouver Laurini MP, Neto ADW. Arbitrage in the Term Structure of Interest Rates: a Bayesian Approach. IER. 2014;6(2):77-99.