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

Yıl 2014, Cilt 6, Sayı 2, 77 - 99, 01.09.2014
https://doi.org/10.33818/ier.278036

Öz

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.

Kaynakça

  • 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.

Yıl 2014, Cilt 6, Sayı 2, 77 - 99, 01.09.2014
https://doi.org/10.33818/ier.278036

Öz

Kaynakça

  • 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.

Ayrıntılar

Konular Sosyal, İşletme
Diğer ID JA48UT39GM
Bölüm Makaleler
Yazarlar

Márcio Poletti Laurini Bu kişi benim


Armênio Dias Westin Neto Bu kişi benim

Yayımlanma Tarihi 1 Eylül 2014
Yayınlandığı Sayı Yıl 2014, Cilt 6, Sayı 2

Kaynak Göster

Bibtex @ { ier278036, journal = {International Econometric Review}, issn = {1308-8793}, eissn = {1308-8815}, address = {Şairler Sokak, No:32/C, Gaziosmanpaşa, Ankara}, publisher = {Ekonometrik Araştırmalar Derneği}, year = {2014}, volume = {6}, pages = {77 - 99}, doi = {10.33818/ier.278036}, title = {Arbitrage in the Term Structure of Interest Rates: a Bayesian Approach}, key = {cite}, author = {Laurini, Márcio Poletti and Neto, Armênio Dias Westin} }
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 . DOI: 10.33818/ier.278036
MLA Laurini, M. P. , Neto, A. D. W. "Arbitrage in the Term Structure of Interest Rates: a Bayesian Approach" . International Econometric Review 6 (2014 ): 77-99 <https://dergipark.org.tr/tr/pub/ier/issue/26397/278036>
Chicago Laurini, M. P. , Neto, A. D. W. "Arbitrage in the Term Structure of Interest Rates: a Bayesian Approach". International Econometric Review 6 (2014 ): 77-99
RIS TY - JOUR T1 - Arbitrage in the Term Structure of Interest Rates: a Bayesian Approach AU - Márcio Poletti Laurini , Armênio Dias Westin Neto Y1 - 2014 PY - 2014 N1 - doi: 10.33818/ier.278036 DO - 10.33818/ier.278036 T2 - International Econometric Review JF - Journal JO - JOR SP - 77 EP - 99 VL - 6 IS - 2 SN - 1308-8793-1308-8815 M3 - doi: 10.33818/ier.278036 UR - https://doi.org/10.33818/ier.278036 Y2 - 2021 ER -
EndNote %0 International Econometric Review Arbitrage in the Term Structure of Interest Rates: a Bayesian Approach %A Márcio Poletti Laurini , Armênio Dias Westin Neto %T Arbitrage in the Term Structure of Interest Rates: a Bayesian Approach %D 2014 %J International Econometric Review %P 1308-8793-1308-8815 %V 6 %N 2 %R doi: 10.33818/ier.278036 %U 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 (Eylül 2014): 77-99 . https://doi.org/10.33818/ier.278036
AMA Laurini M. P. , Neto A. D. W. Arbitrage in the Term Structure of Interest Rates: a Bayesian Approach. IER. 2014; 6(2): 77-99.
Vancouver Laurini M. P. , Neto A. D. W. Arbitrage in the Term Structure of Interest Rates: a Bayesian Approach. International Econometric Review. 2014; 6(2): 77-99.
IEEE M. P. Laurini ve A. D. W. Neto , "Arbitrage in the Term Structure of Interest Rates: a Bayesian Approach", International Econometric Review, c. 6, sayı. 2, ss. 77-99, Eyl. 2014, doi:10.33818/ier.278036