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Stokastik Faiz Oranı Modelleri (CIR / Vasicek) ile Faiz Oranlarının Modellenmesi ve Getiri Eğrisi Tahmini

Yıl 2021, Cilt 36, Sayı 4, 893 - 911, 31.12.2021
https://doi.org/10.24988/ije.807286

Öz

Bu çalışmada stokastik diferansiyel denklemlerine dayanan Vasicek ve CIR modelleri gösterge faiz oranına uygulanarak, modellerin faiz oranı öngörü performansları incelenmiş, getiri eğrisi ve forward verim eğrisi tahmin edilmiştir. Analizler tüm dönemin yanı sıra ICSS algoritmasına bağlı olarak belirlenen farklı volatilite dönemleri dikkate alınarak da yapılmıştır. Modellerin performanslarının analizinde RMSE, ME, MSE, MAE, MAPE ve Theil’s U kriterlerinden yararlanılmıştır. Bulgular, belirgin bir şekilde CIR modelinin performansının Vasicek modelinin performansından daha iyi olduğu sonucuna işaret etmektedir. Çalışma bulgularının para politikası uygulamaları, sabit getirili finansal varlıkların fiyatlanması ve getiri eğrilerinin tahmini gibi konular açısından oldukça önemli bilgiler sunduğu düşünülmektedir.

Kaynakça

  • Ahmed S.E., Nkurunziza S. ve Liu S. (2009). Improved estimation strategy in multi-factor Vasicek model. B. Schipp, W. Kräer W. (Ed.), Statistical Inference, Econometric Analysis and Matrix Algebra içinde (255-270. ss.), Physica:Verlag HD. https://link.Springer.com/chapter/10.1007/978-3-7908-2121-5_17.
  • Albano, G., La Rocca, M. ve Perna, C. (2019). Small sample properties of ml estimator in Vasicek and CIR models: A simulation experiment. Decision in Economics and Finance, 42, 5-19.
  • Almeida, C. ve Vicente, J. (2008). The role of no-arbitrage on forecasting: Lessons from a parametric term structure model. Journal of Banking & Finance, 32, 2695–2705.
  • Anatolyev, S. ve Korepanov, S. (2003). The term structure of Russian ınterest rates. Applied Economics Letters,10,867-870.
  • Ang, A. ve Bekaert, G. (2002). Regime switches in ınterest rates. Journal of Business & Economic Statistics, 20(2),162-182.
  • Babbs, S.H. ve Nowman, K.B. (1998). An application of generalized Vasicek term structure model to UK git-edged market: A Kalman filtering Analysis. Applied Financial Economics,8, 637-644.
  • Bakkaloglu, A., Aziz, T. ve Mahomed, F.M. (2004). Invariant criteria for the zero-coupon bond pricing Vasicek and Cox-Ingersoll-Ross Models. NTMSCI, 5(2), 29-46.
  • Bali, T.G. ve Neftci, S.N. (2003). Disturbing extremal behavior of spot rate dynamics. Journal of Emprical Finance, 10, 455-477.
  • Bao, J. ve Yuan, C. (2013).Long-term behavior of stochastic interest rate models with jumps and memory. Insurance: Mathematics and Economics, 53, 266–272.
  • Bayazıt, D. (2004). Yield curve estimation and prediction with Vasicek model. (Yayımlanmamış Yüksek Lisans Tezi). Orta Doğu Teknik Üniversitesi Uygulamalı Matematik Enstitüsü Finans Matematiği Bölümü, Ankara.
  • Benninga, S. ve Wiener, Z. (1998). Term structure of interest rates. Matematica in Education and Research, 7(2), 1-9.
  • Bianchi, M.L. (2020). Are multi-factor Gaussian term structure models still useful? An empirical analysis on Italian BTPs. Communication in Statistics-Simulation and Computation,12,1-29.
  • Bibbona,E., Panfilo, G. ve Tavella, P. (2008). The Ornstein-Uhlenbeck process as a model of a low pass filtered white noise. Metrologia, 45 (6): 117–126.
  • Brigo D. ve Mercurio F. (2001). Interest rate models theory and practice. Berlin: Springer, Heidelberg.
  • Byers, S.L. ve Nowman,K.B. (1998). Forecasting U.K. and U.S. interest rates using continuous time term structure models. International Review of Financial Analysis, 7(3), 191-206.
  • Chua, C.L., Suardi, S. ve Tsiaplias, S. (2013). Predicting short-term interest rates using Bayesian model averaging: Evidence from weekly and high frequency data. International Journal of Forecasting, 29, 442–455.
  • Cox, J., Ingersoll, J. ve Ross, S. (1985). A theory of the term structure of interest rates. Econometrica, 53, 385–407.
  • Csajkova, A. U. (2007). Calibration of term structure models. (Bitirme Tezi, Comenius University in Bratislava,Slovakya).Erişim adresi: http://www.iam.fmph.uniba.sk/studium/efm/phd /ur ban ova /urbanova-thesis.pdf.
  • Çelik, İ. (2013). Markov zincirlerinin temel özellikleri ve çeşitli uygulamaları. (Yayımlanmamış yüksek lisans tezi). Ordu Üniversitesi Fen Bilimleri Enstitüsü Matematik Anabilim Dalı, Ordu.
  • Dağıstan, Ç. (2010). Quantifying the interest rate risk of bonds by simulation. (Yayımlanmamış yüksek lisans tezi). Boğaziçi Üniversitesi Fen Bilimleri Enstitüsü Endüstri Mühendisliği Anabilim Dalı, İstanbul.
  • Doob, J.L. (1942). The Brownian movement and stochastic equations. Annals of Mathematics, 43(2), 351-369.
  • Georges, P. (2003). The Vasicek and CIR models and the expectation hypothesis of the ınterest rate term structure. Working Papers-Department of Finance Canada 2003-17. Erişim adresi: http: //www.fin.gc.ca/scripts/Publication_Request/request2e.asp?doc =wp2003-17e.pdf.
  • Goard, J. ve Hansen, N. (2004). Comparison of the performance of a time-depended short-ınterest rate model with time-ındependent models. Applied Mathematical Finance, 11,147-164.
  • Herrala, N. (2009). Vasicek interest rate model: Parameter estimation evolution of the short term interest rate and term structure. (Lisans Bitirme Tezi, Lappeenranta University of Technology, Finlandiya). Erişim adresi: https://lutpub.lut.fi/bitstream/handle/10024/43257/nbnfi-fe200901141021.pdf?sequence=3.
  • Inclán, C. ve Tiao, G. C. (1994). Use of cumulative sums of squares for retrospective detection of changes of variance. Journal of The American Statistical Association, 89 (427) , 913–923.
  • Joshi, J.P. ve Swertloff, L. (1999). A users’s guide to ınterest rate models: Application for structured finance. Journal of Risk Finance, 1(1),106-114.
  • Khalique, C. M. ve Motsepa, T. (2018). Lie symmetries, group-invariant solutions and conservation laws of the Vasicek pricing equation of mathematical finance. Physica A: Statistical Mechanics and its Applications, 505, 871-879.
  • Li, J., Clemons, C.B., Young, G.W. ve Zhu, J. (2008). Solutions of two-factor models with variable interest rates. Journal of Computational and Applied Mathematics, 222 (1), 30-41.
  • Ma, C., Liu, J. ve Lan, Q. (2014). Studying term structure of SHIBOR with the two-factor Vasicek model. Abstract and Applied Analysis, 2014,1-7.
  • Mamon, R.S. (2004). Three ways to solve for bond prices in the Vasicek model. Journal of Applied Mathematics and Decision Sciences, 8(1), 1–14.
  • Moreno, M. ve Platania, F. (2015). A cyclical square-root model for the term structure of ınterest rates.European Journal of Operational Research, 241(1), 109-121.
  • Nath, P. ve Nowman, B. (2001). Estimates of the continuous time Cox-Ingersoll-Ross term structure model: Further results for the UK gilt-edged market. Applied Economics Lettres, 8, 85-88.
  • Neftcı, S.N.(2000). Value-at-risk calculations, extreme events, and tail estimation. The Journal of Derivatives, 7 (3) , 23-38.
  • Nowman, K.B. (2001). Gaussian estimation and forecasting of multi-factor term structure models with an application to Japan and the United Kingdom. Asia-Pacific Financial Markets, 8, 23-34.
  • Nowman, K.B. ve Saltoğlu, B. (2003). Continuous time and nonparametric modelling of U.S. interest rate models. International Review of Financial Analysis,12, 25-34.
  • Orlando, G., Mininni, R.M. ve Bufalo, M. (2019a). A new approach to forecast market interest rates through the CIR Model. Studies in Economics and Finance, 37 (2), 267-292.
  • Orlando, G., Mininni, R.M., Bufalo, M. (2019b). Interest rates calibration with a CIR model. The Journal of Risk Finance, 20 (4), 370-387.
  • Rogers, L.C.G. ve Stummer, W. (2000). Consistent fitting of one-factor models to ınterest rate data.Insurance: Mathematics and Economics,27, 45-63.
  • Önalan, Ö. (2009). Vasicek ve CIR modelleri kullanılarak oynaklık ve faiz oranlarının modellenmesi. Marmara Üniversitesi İ.İ.B.F. Dergisi, 27 (2), 329-344.
  • Sansó, A., Aragó, V. ve Carrion-I Silvestre, J. L. (2004). Testing for change in the unconditional variance of financial time series. Revista de Economía Financiera, 4, 32–53.
  • Schulmerich, M. (2005). Real options valuation. Berlin: Springer, Heidelberg.
  • Sinkala, W., Leach, P.G.L. ve O’hara, J.G.O. (2008). Zero-coupon bond prices in the Vasicek and CIR models: Their computations as group-ınvariant solutions. Mathematical Methods in the Applied Sciences,31,665-678.
  • Sypkens, R. (2010). Risk properties and parameter estimation on a mean reversion and GARCH models. (Yüksek Lisans Tezi, University of South Africa, Güney Afrika). Erişim adresi: http://uir.unisa.ac.za /bitst ream/handle/1 0500/4049/ disserta tion sypkens_r.pdf.
  • Şahin, H. ve Genç, İ.H. (2009).Kısa dönem faiz modellerinin Türkiye için ampirik analizi. BDDK Bankacılık ve Finansal Piyasalar, 3 (2), 107-119.
  • Tse, Y. K. (1995). Stochastic models of interest rates in economics, finance and actuarial science. Paper presented at the International Congress on Modelling and Simulation, Newcastle, New South Wales, Australia.https://ink.library.smu.edu.sg/soe_research/714
  • van Elen, E. (2010). Term structure of forecasting. Does a good fit imply reasonable simulation results ?. (Lisans Bitirme Tezi, Tilburg University, Hollanda). Erişim adresi: https://www.netspar.nl/assets/uploads/BA_Emilevan_Elen_2010.pdf.
  • Vasicek, O. (1977). An equilibrium characterization of the term structure. Journal of Financial Economics, 5, 177–188.
  • Yolcu, Y. (2005). One-factor interest rate models: Analytic solutions and approximations. (Yayımlanmamış yüksek lisans tezi). Orta Doğu Teknik Üniversitesi Uygulamalı Matematik Enstitüsü, Finans Matematiği Bölümü, Ankara.
  • Zeytun, S. ve Gupta, A. (2007). A comparative study of the Vasicek and the CIR model of the short rate. Technical Report 124, Fraunhofer (ITWM),Nr. 124. Erişim adresi: https://kluedo.ub.uni-kl.de/frontdoor/deliver/index/docId/1979/file/bericht124.pdf.
  • Zeytun, S. (2005). Stochastic volatility, a new approach for Vasicek model with stochastic volatility. (Yayımlanmamış Yüksek Lisans Tezi). Orta Doğu Teknik Üniversitesi Uygulamalı Matematik Enstitüsü Finans Matematiği Bölümü, Anakara.
  • Zhang, Y.G., Su, Y.P. ve Yang, B.C. (2009). An empirical analysis on term structure of SHIBOR using Vasicek and CIR models. Statistics & Information Forum, 24 (6), 44-48.
  • Zhou,N. ve Mamon,R. (2012). An accessible implementation of interest rate models with markov-switching. Expert Systems with Applications,39,4679-4689.

Modelling Interest Rates, and Forecasting the Yield Curve with Stochastic Interest Rate Models (CIR and Vasicek)

Yıl 2021, Cilt 36, Sayı 4, 893 - 911, 31.12.2021
https://doi.org/10.24988/ije.807286

Öz

In this study, the CIR and Vasicek models, both of which are based on stochastic differential equations, are applied to benchmark government bond interest rates. After this, the interest rate forecasting performances of these models are examined for whole periods as well as for sub-periods determined based on the ICSS algorithm. RMSE, MSE, MAE, ME, and MAPE loss functions along with Theil’s U method are used to analyse the forecasting performances of the models. The results show that the CIR model performs better than the Vasicek model. The findings of the study have important implications for monetary policy applications, fixed income security valuations, and yield curve estimations.

Kaynakça

  • Ahmed S.E., Nkurunziza S. ve Liu S. (2009). Improved estimation strategy in multi-factor Vasicek model. B. Schipp, W. Kräer W. (Ed.), Statistical Inference, Econometric Analysis and Matrix Algebra içinde (255-270. ss.), Physica:Verlag HD. https://link.Springer.com/chapter/10.1007/978-3-7908-2121-5_17.
  • Albano, G., La Rocca, M. ve Perna, C. (2019). Small sample properties of ml estimator in Vasicek and CIR models: A simulation experiment. Decision in Economics and Finance, 42, 5-19.
  • Almeida, C. ve Vicente, J. (2008). The role of no-arbitrage on forecasting: Lessons from a parametric term structure model. Journal of Banking & Finance, 32, 2695–2705.
  • Anatolyev, S. ve Korepanov, S. (2003). The term structure of Russian ınterest rates. Applied Economics Letters,10,867-870.
  • Ang, A. ve Bekaert, G. (2002). Regime switches in ınterest rates. Journal of Business & Economic Statistics, 20(2),162-182.
  • Babbs, S.H. ve Nowman, K.B. (1998). An application of generalized Vasicek term structure model to UK git-edged market: A Kalman filtering Analysis. Applied Financial Economics,8, 637-644.
  • Bakkaloglu, A., Aziz, T. ve Mahomed, F.M. (2004). Invariant criteria for the zero-coupon bond pricing Vasicek and Cox-Ingersoll-Ross Models. NTMSCI, 5(2), 29-46.
  • Bali, T.G. ve Neftci, S.N. (2003). Disturbing extremal behavior of spot rate dynamics. Journal of Emprical Finance, 10, 455-477.
  • Bao, J. ve Yuan, C. (2013).Long-term behavior of stochastic interest rate models with jumps and memory. Insurance: Mathematics and Economics, 53, 266–272.
  • Bayazıt, D. (2004). Yield curve estimation and prediction with Vasicek model. (Yayımlanmamış Yüksek Lisans Tezi). Orta Doğu Teknik Üniversitesi Uygulamalı Matematik Enstitüsü Finans Matematiği Bölümü, Ankara.
  • Benninga, S. ve Wiener, Z. (1998). Term structure of interest rates. Matematica in Education and Research, 7(2), 1-9.
  • Bianchi, M.L. (2020). Are multi-factor Gaussian term structure models still useful? An empirical analysis on Italian BTPs. Communication in Statistics-Simulation and Computation,12,1-29.
  • Bibbona,E., Panfilo, G. ve Tavella, P. (2008). The Ornstein-Uhlenbeck process as a model of a low pass filtered white noise. Metrologia, 45 (6): 117–126.
  • Brigo D. ve Mercurio F. (2001). Interest rate models theory and practice. Berlin: Springer, Heidelberg.
  • Byers, S.L. ve Nowman,K.B. (1998). Forecasting U.K. and U.S. interest rates using continuous time term structure models. International Review of Financial Analysis, 7(3), 191-206.
  • Chua, C.L., Suardi, S. ve Tsiaplias, S. (2013). Predicting short-term interest rates using Bayesian model averaging: Evidence from weekly and high frequency data. International Journal of Forecasting, 29, 442–455.
  • Cox, J., Ingersoll, J. ve Ross, S. (1985). A theory of the term structure of interest rates. Econometrica, 53, 385–407.
  • Csajkova, A. U. (2007). Calibration of term structure models. (Bitirme Tezi, Comenius University in Bratislava,Slovakya).Erişim adresi: http://www.iam.fmph.uniba.sk/studium/efm/phd /ur ban ova /urbanova-thesis.pdf.
  • Çelik, İ. (2013). Markov zincirlerinin temel özellikleri ve çeşitli uygulamaları. (Yayımlanmamış yüksek lisans tezi). Ordu Üniversitesi Fen Bilimleri Enstitüsü Matematik Anabilim Dalı, Ordu.
  • Dağıstan, Ç. (2010). Quantifying the interest rate risk of bonds by simulation. (Yayımlanmamış yüksek lisans tezi). Boğaziçi Üniversitesi Fen Bilimleri Enstitüsü Endüstri Mühendisliği Anabilim Dalı, İstanbul.
  • Doob, J.L. (1942). The Brownian movement and stochastic equations. Annals of Mathematics, 43(2), 351-369.
  • Georges, P. (2003). The Vasicek and CIR models and the expectation hypothesis of the ınterest rate term structure. Working Papers-Department of Finance Canada 2003-17. Erişim adresi: http: //www.fin.gc.ca/scripts/Publication_Request/request2e.asp?doc =wp2003-17e.pdf.
  • Goard, J. ve Hansen, N. (2004). Comparison of the performance of a time-depended short-ınterest rate model with time-ındependent models. Applied Mathematical Finance, 11,147-164.
  • Herrala, N. (2009). Vasicek interest rate model: Parameter estimation evolution of the short term interest rate and term structure. (Lisans Bitirme Tezi, Lappeenranta University of Technology, Finlandiya). Erişim adresi: https://lutpub.lut.fi/bitstream/handle/10024/43257/nbnfi-fe200901141021.pdf?sequence=3.
  • Inclán, C. ve Tiao, G. C. (1994). Use of cumulative sums of squares for retrospective detection of changes of variance. Journal of The American Statistical Association, 89 (427) , 913–923.
  • Joshi, J.P. ve Swertloff, L. (1999). A users’s guide to ınterest rate models: Application for structured finance. Journal of Risk Finance, 1(1),106-114.
  • Khalique, C. M. ve Motsepa, T. (2018). Lie symmetries, group-invariant solutions and conservation laws of the Vasicek pricing equation of mathematical finance. Physica A: Statistical Mechanics and its Applications, 505, 871-879.
  • Li, J., Clemons, C.B., Young, G.W. ve Zhu, J. (2008). Solutions of two-factor models with variable interest rates. Journal of Computational and Applied Mathematics, 222 (1), 30-41.
  • Ma, C., Liu, J. ve Lan, Q. (2014). Studying term structure of SHIBOR with the two-factor Vasicek model. Abstract and Applied Analysis, 2014,1-7.
  • Mamon, R.S. (2004). Three ways to solve for bond prices in the Vasicek model. Journal of Applied Mathematics and Decision Sciences, 8(1), 1–14.
  • Moreno, M. ve Platania, F. (2015). A cyclical square-root model for the term structure of ınterest rates.European Journal of Operational Research, 241(1), 109-121.
  • Nath, P. ve Nowman, B. (2001). Estimates of the continuous time Cox-Ingersoll-Ross term structure model: Further results for the UK gilt-edged market. Applied Economics Lettres, 8, 85-88.
  • Neftcı, S.N.(2000). Value-at-risk calculations, extreme events, and tail estimation. The Journal of Derivatives, 7 (3) , 23-38.
  • Nowman, K.B. (2001). Gaussian estimation and forecasting of multi-factor term structure models with an application to Japan and the United Kingdom. Asia-Pacific Financial Markets, 8, 23-34.
  • Nowman, K.B. ve Saltoğlu, B. (2003). Continuous time and nonparametric modelling of U.S. interest rate models. International Review of Financial Analysis,12, 25-34.
  • Orlando, G., Mininni, R.M. ve Bufalo, M. (2019a). A new approach to forecast market interest rates through the CIR Model. Studies in Economics and Finance, 37 (2), 267-292.
  • Orlando, G., Mininni, R.M., Bufalo, M. (2019b). Interest rates calibration with a CIR model. The Journal of Risk Finance, 20 (4), 370-387.
  • Rogers, L.C.G. ve Stummer, W. (2000). Consistent fitting of one-factor models to ınterest rate data.Insurance: Mathematics and Economics,27, 45-63.
  • Önalan, Ö. (2009). Vasicek ve CIR modelleri kullanılarak oynaklık ve faiz oranlarının modellenmesi. Marmara Üniversitesi İ.İ.B.F. Dergisi, 27 (2), 329-344.
  • Sansó, A., Aragó, V. ve Carrion-I Silvestre, J. L. (2004). Testing for change in the unconditional variance of financial time series. Revista de Economía Financiera, 4, 32–53.
  • Schulmerich, M. (2005). Real options valuation. Berlin: Springer, Heidelberg.
  • Sinkala, W., Leach, P.G.L. ve O’hara, J.G.O. (2008). Zero-coupon bond prices in the Vasicek and CIR models: Their computations as group-ınvariant solutions. Mathematical Methods in the Applied Sciences,31,665-678.
  • Sypkens, R. (2010). Risk properties and parameter estimation on a mean reversion and GARCH models. (Yüksek Lisans Tezi, University of South Africa, Güney Afrika). Erişim adresi: http://uir.unisa.ac.za /bitst ream/handle/1 0500/4049/ disserta tion sypkens_r.pdf.
  • Şahin, H. ve Genç, İ.H. (2009).Kısa dönem faiz modellerinin Türkiye için ampirik analizi. BDDK Bankacılık ve Finansal Piyasalar, 3 (2), 107-119.
  • Tse, Y. K. (1995). Stochastic models of interest rates in economics, finance and actuarial science. Paper presented at the International Congress on Modelling and Simulation, Newcastle, New South Wales, Australia.https://ink.library.smu.edu.sg/soe_research/714
  • van Elen, E. (2010). Term structure of forecasting. Does a good fit imply reasonable simulation results ?. (Lisans Bitirme Tezi, Tilburg University, Hollanda). Erişim adresi: https://www.netspar.nl/assets/uploads/BA_Emilevan_Elen_2010.pdf.
  • Vasicek, O. (1977). An equilibrium characterization of the term structure. Journal of Financial Economics, 5, 177–188.
  • Yolcu, Y. (2005). One-factor interest rate models: Analytic solutions and approximations. (Yayımlanmamış yüksek lisans tezi). Orta Doğu Teknik Üniversitesi Uygulamalı Matematik Enstitüsü, Finans Matematiği Bölümü, Ankara.
  • Zeytun, S. ve Gupta, A. (2007). A comparative study of the Vasicek and the CIR model of the short rate. Technical Report 124, Fraunhofer (ITWM),Nr. 124. Erişim adresi: https://kluedo.ub.uni-kl.de/frontdoor/deliver/index/docId/1979/file/bericht124.pdf.
  • Zeytun, S. (2005). Stochastic volatility, a new approach for Vasicek model with stochastic volatility. (Yayımlanmamış Yüksek Lisans Tezi). Orta Doğu Teknik Üniversitesi Uygulamalı Matematik Enstitüsü Finans Matematiği Bölümü, Anakara.
  • Zhang, Y.G., Su, Y.P. ve Yang, B.C. (2009). An empirical analysis on term structure of SHIBOR using Vasicek and CIR models. Statistics & Information Forum, 24 (6), 44-48.
  • Zhou,N. ve Mamon,R. (2012). An accessible implementation of interest rate models with markov-switching. Expert Systems with Applications,39,4679-4689.

Ayrıntılar

Birincil Dil Türkçe
Konular İşletme
Bölüm Makaleler
Yazarlar

Önder BÜBERKÖKÜ (Sorumlu Yazar)
Yüzüncü Yıl Üniversitesi
0000-0002-7140-557X
Türkiye

Yayımlanma Tarihi 31 Aralık 2021
Başvuru Tarihi 7 Ekim 2020
Kabul Tarihi 30 Eylül 2021
Yayınlandığı Sayı Yıl 2021, Cilt 36, Sayı 4

Kaynak Göster

Bibtex @araştırma makalesi { ije807286, journal = {İzmir İktisat Dergisi}, issn = {1308-8173}, eissn = {1308-8505}, address = {Dokuz Eylül Üniversitesi İktisadi ve İdari Bilimler Fakültesi Buca - İZMİR}, publisher = {Dokuz Eylül Üniversitesi}, year = {2021}, volume = {36}, number = {4}, pages = {893 - 911}, doi = {10.24988/ije.807286}, title = {Stokastik Faiz Oranı Modelleri (CIR / Vasicek) ile Faiz Oranlarının Modellenmesi ve Getiri Eğrisi Tahmini}, key = {cite}, author = {Büberkökü, Önder} }
APA Büberkökü, Ö. (2021). Stokastik Faiz Oranı Modelleri (CIR / Vasicek) ile Faiz Oranlarının Modellenmesi ve Getiri Eğrisi Tahmini . İzmir İktisat Dergisi , 36 (4) , 893-911 . DOI: 10.24988/ije.807286
MLA Büberkökü, Ö. "Stokastik Faiz Oranı Modelleri (CIR / Vasicek) ile Faiz Oranlarının Modellenmesi ve Getiri Eğrisi Tahmini" . İzmir İktisat Dergisi 36 (2021 ): 893-911 <https://dergipark.org.tr/tr/pub/ije/issue/64777/807286>
Chicago Büberkökü, Ö. "Stokastik Faiz Oranı Modelleri (CIR / Vasicek) ile Faiz Oranlarının Modellenmesi ve Getiri Eğrisi Tahmini". İzmir İktisat Dergisi 36 (2021 ): 893-911
RIS TY - JOUR T1 - Stokastik Faiz Oranı Modelleri (CIR / Vasicek) ile Faiz Oranlarının Modellenmesi ve Getiri Eğrisi Tahmini AU - Önder Büberkökü Y1 - 2021 PY - 2021 N1 - doi: 10.24988/ije.807286 DO - 10.24988/ije.807286 T2 - İzmir İktisat Dergisi JF - Journal JO - JOR SP - 893 EP - 911 VL - 36 IS - 4 SN - 1308-8173-1308-8505 M3 - doi: 10.24988/ije.807286 UR - https://doi.org/10.24988/ije.807286 Y2 - 2021 ER -
EndNote %0 İzmir İktisat Dergisi Stokastik Faiz Oranı Modelleri (CIR / Vasicek) ile Faiz Oranlarının Modellenmesi ve Getiri Eğrisi Tahmini %A Önder Büberkökü %T Stokastik Faiz Oranı Modelleri (CIR / Vasicek) ile Faiz Oranlarının Modellenmesi ve Getiri Eğrisi Tahmini %D 2021 %J İzmir İktisat Dergisi %P 1308-8173-1308-8505 %V 36 %N 4 %R doi: 10.24988/ije.807286 %U 10.24988/ije.807286
ISNAD Büberkökü, Önder . "Stokastik Faiz Oranı Modelleri (CIR / Vasicek) ile Faiz Oranlarının Modellenmesi ve Getiri Eğrisi Tahmini". İzmir İktisat Dergisi 36 / 4 (Aralık 2021): 893-911 . https://doi.org/10.24988/ije.807286
AMA Büberkökü Ö. Stokastik Faiz Oranı Modelleri (CIR / Vasicek) ile Faiz Oranlarının Modellenmesi ve Getiri Eğrisi Tahmini. ije. 2021; 36(4): 893-911.
Vancouver Büberkökü Ö. Stokastik Faiz Oranı Modelleri (CIR / Vasicek) ile Faiz Oranlarının Modellenmesi ve Getiri Eğrisi Tahmini. İzmir İktisat Dergisi. 2021; 36(4): 893-911.
IEEE Ö. Büberkökü , "Stokastik Faiz Oranı Modelleri (CIR / Vasicek) ile Faiz Oranlarının Modellenmesi ve Getiri Eğrisi Tahmini", İzmir İktisat Dergisi, c. 36, sayı. 4, ss. 893-911, Ara. 2021, doi:10.24988/ije.807286

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