IDEAS home Printed from https://ideas.repec.org/p/rdg/icmadp/icma-dp2002-03.html
   My bibliography  Save this paper

Disturbing Extremal Behavior of Spot Rate Dynamics

Author

Listed:
  • Turan G. Bali

    (City University of New York, USA)

  • Salih N. Neftci

    (City University of New York, USA and ICMA Centre, University of Reading, UK)

Abstract

This paper presents a study of extreme interest rate movements in the U.S. Federal Funds market over almost a half century of daily observations from the mid 1950s through the end of 2000. We analyze the fluctuations of the maximal and minimal changes in short term interest rates and test the significance of time-varying paths followed by the mean and volatility of extremes. We formally determine the relevance of introducing trend and serial correlation in the mean, and of incorporating the level and GARCH effects in the volatility of extreme changes in the federal funds rate. The empirical findings indicate the existence of volatility clustering in the standard deviation of extremes, and a significantly positive relationship between the level and the volatility of extremes. The results point to the presence of an autoregressive process in the means of both local maxima and local minima values. The paper proposes a conditional extreme value approach to calculating value at risk by specifying the location and scale parameters of the generalized Pareto distribution as a function of past information. Based on the estimated VaR thresholds, the statistical theory of extremes is found to provide more accurate estimates of the rate of occurrence and the size of extreme observations.

Suggested Citation

  • Turan G. Bali & Salih N. Neftci, 2002. "Disturbing Extremal Behavior of Spot Rate Dynamics," ICMA Centre Discussion Papers in Finance icma-dp2002-03, Henley Business School, University of Reading.
  • Handle: RePEc:rdg:icmadp:icma-dp2002-03
    as

    Download full text from publisher

    File URL: http://www.icmacentre.ac.uk/pdf/discussion/DP2002-03.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Ait-Sahalia, Yacine, 1996. "Testing Continuous-Time Models of the Spot Interest Rate," The Review of Financial Studies, Society for Financial Studies, vol. 9(2), pages 385-426.
    2. Christian Gollier & Pierre-François Koehl & Jean-Charles Rochet, 1996. "Risk-Taking Behavior with Limited Liability and Risk Aversion," Center for Financial Institutions Working Papers 96-13, Wharton School Center for Financial Institutions, University of Pennsylvania.
    3. McNeil, Alexander J. & Frey, Rudiger, 2000. "Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 271-300, November.
    4. Conley, Timothy G, et al, 1997. "Short-Term Interest Rates as Subordinated Diffusions," The Review of Financial Studies, Society for Financial Studies, vol. 10(3), pages 525-577.
    5. Jansen, Dennis W & de Vries, Casper G, 1991. "On the Frequency of Large Stock Returns: Putting Booms and Busts into Perspective," The Review of Economics and Statistics, MIT Press, vol. 73(1), pages 18-24, February.
    6. Gourieroux, C. & Laurent, J. P. & Scaillet, O., 2000. "Sensitivity analysis of Values at Risk," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 225-245, November.
    7. Brenner, Robin J. & Harjes, Richard H. & Kroner, Kenneth F., 1996. "Another Look at Models of the Short-Term Interest Rate," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 31(1), pages 85-107, March.
    8. Christian Gourieroux & Joanna Jasiak, 1998. "Truncated Maximum Likelihood and Nonparametric Tail Analysis," Working Papers 98-25, Center for Research in Economics and Statistics.
    9. Ait-Sahalia, Yacine, 1996. "Nonparametric Pricing of Interest Rate Derivative Securities," Econometrica, Econometric Society, vol. 64(3), pages 527-560, May.
    10. Casper De Vries & Jon Danielsson & Casper G, de Vries, 1996. "Tail Index and Quantile Estimation with Very High Frequency Data," CESifo Working Paper Series 116, CESifo.
    11. Phillip Kearns & Adrian Pagan, 1997. "Estimating The Density Tail Index For Financial Time Series," The Review of Economics and Statistics, MIT Press, vol. 79(2), pages 171-175, May.
    12. Jansen, Dennis W. & Koedijk, Kees G. & de Vries, Casper G., 2000. "Portfolio selection with limited downside risk," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 247-269, November.
    13. Longin, Francois M., 2000. "From value at risk to stress testing: The extreme value approach," Journal of Banking & Finance, Elsevier, vol. 24(7), pages 1097-1130, July.
    14. Chan, K C, et al, 1992. "An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," Journal of Finance, American Finance Association, vol. 47(3), pages 1209-1227, July.
    15. Parkinson, Michael, 1980. "The Extreme Value Method for Estimating the Variance of the Rate of Return," The Journal of Business, University of Chicago Press, vol. 53(1), pages 61-65, January.
    16. McCulloch, J Huston, 1997. "Measuring Tail Thickness to Estimate the Stable Index Alpha: A Critique," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(1), pages 74-81, January.
    17. Longin, Francois M, 1996. "The Asymptotic Distribution of Extreme Stock Market Returns," The Journal of Business, University of Chicago Press, vol. 69(3), pages 383-408, July.
    18. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    19. Andersen, Torben G. & Lund, Jesper, 1997. "Estimating continuous-time stochastic volatility models of the short-term interest rate," Journal of Econometrics, Elsevier, vol. 77(2), pages 343-377, April.
    20. Kees G. Koedijk & François G. J. A. Nissen & Peter C. Schotman & Christian C. P. Wolff, 1997. "The Dynamics of Short-Term Interest Rate Volatility Reconsidered," Review of Finance, European Finance Association, vol. 1(1), pages 105-130.
    21. Stanton, Richard, 1997. "A Nonparametric Model of Term Structure Dynamics and the Market Price of Interest Rate Risk," Journal of Finance, American Finance Association, vol. 52(5), pages 1973-2002, December.
    22. David F. Babbel & Anthony M. Santomero, 1997. "Risk Management by Insurers: An Analysis of the Process," Center for Financial Institutions Working Papers 96-16, Wharton School Center for Financial Institutions, University of Pennsylvania.
    23. Longstaff, Francis A & Schwartz, Eduardo S, 1992. "Interest Rate Volatility and the Term Structure: A Two-Factor General Equilibrium Model," Journal of Finance, American Finance Association, vol. 47(4), pages 1259-1282, September.
    24. Bali, Turan G., 2000. "Testing the Empirical Performance of Stochastic Volatility Models of the Short-Term Interest Rate," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 35(2), pages 191-215, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Li, Longqing, 2017. "A Comparative Study of GARCH and EVT Model in Modeling Value-at-Risk," MPRA Paper 85645, University Library of Munich, Germany.
    2. Straetmans, Stefan & Chaudhry, Sajid M., 2015. "Tail risk and systemic risk of US and Eurozone financial institutions in the wake of the global financial crisis," Journal of International Money and Finance, Elsevier, vol. 58(C), pages 191-223.
    3. Karmakar, Madhusudan & Shukla, Girja K., 2015. "Managing extreme risk in some major stock markets: An extreme value approach," International Review of Economics & Finance, Elsevier, vol. 35(C), pages 1-25.
    4. Turan G. Bali, 2007. "A Generalized Extreme Value Approach to Financial Risk Measurement," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(7), pages 1613-1649, October.
    5. Krehbiel, Tim & Adkins, Lee C., 2008. "Extreme daily changes in U.S. Dollar London inter-bank offer rates," International Review of Economics & Finance, Elsevier, vol. 17(3), pages 397-411.
    6. Paraschiv, Florentina & Mudry, Pierre-Antoine & Andries, Alin Marius, 2015. "Stress-testing for portfolios of commodity futures," Economic Modelling, Elsevier, vol. 50(C), pages 9-18.
    7. Samit Paul & Madhusudan Karmakar, 2017. "Relative Efficiency of Component GARCH-EVT Approach in Managing Intraday Market Risk," Multinational Finance Journal, Multinational Finance Journal, vol. 21(4), pages 247-283, December.
    8. Karmakar, Madhusudan & Paul, Samit, 2016. "Intraday risk management in International stock markets: A conditional EVT approach," International Review of Financial Analysis, Elsevier, vol. 44(C), pages 34-55.
    9. Yuan, Ying & Zhuang, Xin-tian & Liu, Zhi-ying & Huang, Wei-qiang, 2012. "Time-clustering behavior of sharp fluctuation sequences in Chinese stock markets," Chaos, Solitons & Fractals, Elsevier, vol. 45(6), pages 838-845.
    10. Chebbi, Ali & Hedhli, Amel, 2022. "Revisiting the accuracy of standard VaR methods for risk assessment: Using the Copula–EVT multidimensional approach for stock markets in the MENA region," The Quarterly Review of Economics and Finance, Elsevier, vol. 84(C), pages 430-445.
    11. Marco Rocco, 2011. "Extreme value theory for finance: a survey," Questioni di Economia e Finanza (Occasional Papers) 99, Bank of Italy, Economic Research and International Relations Area.
    12. Benjamin R. Auer & Benjamin Mögel, 2016. "How Accurate are Modern Value-at-Risk Estimators Derived from Extreme Value Theory?," CESifo Working Paper Series 6288, CESifo.
    13. Turan Bali & Panayiotis Theodossiou, 2007. "A conditional-SGT-VaR approach with alternative GARCH models," Annals of Operations Research, Springer, vol. 151(1), pages 241-267, April.
    14. Aditya Banerjee & Samit Paul, 2024. "Idiosyncrasies of Intraday Risk in Emerging and Developed Markets: Efficacy of the MCS-GARCH Model and Extreme Value Theory," Global Business Review, International Management Institute, vol. 25(2), pages 468-490, April.
    15. S. T. M. Straetmans & W. F. C. Verschoor & C. C. P. Wolff, 2008. "Extreme US stock market fluctuations in the wake of 9|11," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(1), pages 17-42.
    16. James W. Taylor & Keming Yu, 2016. "Using auto-regressive logit models to forecast the exceedance probability for financial risk management," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 179(4), pages 1069-1092, October.
    17. Benjamin Mögel & Benjamin R. Auer, 2018. "How accurate are modern Value-at-Risk estimators derived from extreme value theory?," Review of Quantitative Finance and Accounting, Springer, vol. 50(4), pages 979-1030, May.
    18. Basu, Sanjay, 2011. "Comparing simulation models for market risk stress testing," European Journal of Operational Research, Elsevier, vol. 213(1), pages 329-339, August.
    19. Xue Deng & Ying Liang, 2023. "Robust Portfolio Optimization Based on Semi-Parametric ARMA-TGARCH-EVT Model with Mixed Copula Using WCVaR," Computational Economics, Springer;Society for Computational Economics, vol. 61(1), pages 267-294, January.
    20. Bali, Turan G. & Weinbaum, David, 2007. "A conditional extreme value volatility estimator based on high-frequency returns," Journal of Economic Dynamics and Control, Elsevier, vol. 31(2), pages 361-397, February.
    21. Youssef, Manel & Belkacem, Lotfi & Mokni, Khaled, 2015. "Value-at-Risk estimation of energy commodities: A long-memory GARCH–EVT approach," Energy Economics, Elsevier, vol. 51(C), pages 99-110.
    22. Tolikas, Konstantinos, 2014. "Unexpected tails in risk measurement: Some international evidence," Journal of Banking & Finance, Elsevier, vol. 40(C), pages 476-493.
    23. Allen, Linda & Bali, Turan G., 2007. "Cyclicality in catastrophic and operational risk measurements," Journal of Banking & Finance, Elsevier, vol. 31(4), pages 1191-1235, April.
    24. Manel Youssef & Lotfi Belkacem & Khaled Mokni, 2015. "Extreme Value Theory and long-memory-GARCH Framework: Application to Stock Market," International Journal of Economics and Empirical Research (IJEER), The Economics and Social Development Organization (TESDO), vol. 3(8), pages 371-388, August.
    25. Riedel, Christoph & Wagner, Niklas, 2015. "Is risk higher during non-trading periods? The risk trade-off for intraday versus overnight market returns," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 39(C), pages 53-64.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bali, Turan G., 2003. "Modeling the stochastic behavior of short-term interest rates: Pricing implications for discount bonds," Journal of Banking & Finance, Elsevier, vol. 27(2), pages 201-228, February.
    2. Bali, Turan G. & Wu, Liuren, 2006. "A comprehensive analysis of the short-term interest-rate dynamics," Journal of Banking & Finance, Elsevier, vol. 30(4), pages 1269-1290, April.
    3. repec:wyi:journl:002108 is not listed on IDEAS
    4. Teresa Corzo Santamaría & Javier Gómez Biscarri, 2005. "Nonparametric estimation of convergence of interest rates: Effects on bond pricing," Spanish Economic Review, Springer;Spanish Economic Association, vol. 7(3), pages 167-190, September.
    5. Zongwu Cai & Yongmiao Hong, 2013. "Some Recent Developments in Nonparametric Finance," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    6. Antonio Mele, 2003. "Fundamental Properties of Bond Prices in Models of the Short-Term Rate," The Review of Financial Studies, Society for Financial Studies, vol. 16(3), pages 679-716, July.
    7. repec:wyi:journl:002109 is not listed on IDEAS
    8. Jun Yu & Peter C. B. Phillips, 2001. "A Gaussian approach for continuous time models of the short-term interest rate," Econometrics Journal, Royal Economic Society, vol. 4(2), pages 1-3.
    9. Cai, Zongwu & Hong, Yongmiao, 2003. "Nonparametric Methods in Continuous-Time Finance: A Selective Review," SFB 373 Discussion Papers 2003,15, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    10. Das, Sanjiv R., 2002. "The surprise element: jumps in interest rates," Journal of Econometrics, Elsevier, vol. 106(1), pages 27-65, January.
    11. Christiansen, Charlotte, 2008. "Level-ARCH short rate models with regime switching: Bivariate modeling of US and European short rates," International Review of Financial Analysis, Elsevier, vol. 17(5), pages 925-948, December.
    12. Czellar, Veronika & Karolyi, G. Andrew & Ronchetti, Elvezio, 2007. "Indirect robust estimation of the short-term interest rate process," Journal of Empirical Finance, Elsevier, vol. 14(4), pages 546-563, September.
    13. Kalimipalli, Madhu & Susmel, Raul, 2004. "Regime-switching stochastic volatility and short-term interest rates," Journal of Empirical Finance, Elsevier, vol. 11(3), pages 309-329, June.
    14. Al-Zoubi, Haitham A., 2009. "Short-term spot rate models with nonparametric deterministic drift," The Quarterly Review of Economics and Finance, Elsevier, vol. 49(3), pages 731-747, August.
    15. Hong, Yongmiao & Lin, Hai & Wang, Shouyang, 2010. "Modeling the dynamics of Chinese spot interest rates," Journal of Banking & Finance, Elsevier, vol. 34(5), pages 1047-1061, May.
    16. Turan Bali, 2007. "Modeling the dynamics of interest rate volatility with skewed fat-tailed distributions," Annals of Operations Research, Springer, vol. 151(1), pages 151-178, April.
    17. Dennis Kristensen, 2004. "A Semiparametric Single-Factor Model of the Term Structure," FMG Discussion Papers dp501, Financial Markets Group.
    18. V. Cvsa & P. Ritchken, 2001. "Pricing Claims Under GARCH-Level Dependent Interest Rate Processes," Management Science, INFORMS, vol. 47(12), pages 1693-1711, December.
    19. Jin-Chuan Duan & Kris Jacobs, 2001. "Short and Long Memory in Equilibrium Interest Rate Dynamics," CIRANO Working Papers 2001s-22, CIRANO.
    20. Sun, Licheng, 2005. "Regime shifts in interest rate volatility," Journal of Empirical Finance, Elsevier, vol. 12(3), pages 418-434, June.
    21. Duan, Jin-Chuan & Jacobs, Kris, 2008. "Is long memory necessary? An empirical investigation of nonnegative interest rate processes," Journal of Empirical Finance, Elsevier, vol. 15(3), pages 567-581, June.
    22. repec:wyi:journl:002118 is not listed on IDEAS
    23. Andrew D. Sanford & Gael Martin, 2004. "Bayesian Analysis of Continuous Time Models of the Australian Short Rate," Monash Econometrics and Business Statistics Working Papers 11/04, Monash University, Department of Econometrics and Business Statistics.

    More about this item

    Keywords

    extreme value theory; volatility; interest rates; value at risk;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:rdg:icmadp:icma-dp2002-03. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Marie Pearson (email available below). General contact details of provider: https://edirc.repec.org/data/bsrdguk.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.