Remember Me
Or use your Academic/Social account:


Or use your Academic/Social account:


You have just completed your registration at OpenAire.

Before you can login to the site, you will need to activate your account. An e-mail will be sent to you with the proper instructions.


Please note that this site is currently undergoing Beta testing.
Any new content you create is not guaranteed to be present to the final version of the site upon release.

Thank you for your patience,
OpenAire Dev Team.

Close This Message


Verify Password:
Verify E-mail:
*All Fields Are Required.
Please Verify You Are Human:
fbtwitterlinkedinvimeoflicker grey 14rssslideshare1
Languages: English
Types: Doctoral thesis
Subjects: HB
A new class of interest rate models is proposed where the main driving terms for the large\ud scale dynamics of the system are deterministic. As an example, an economically motivated two\ud factor model of the term structure is presented that generalises existing stochastic mean term\ud structure models.\ud By allowing a certain parameter to acquire dynamical behaviour the model is extended to\ud three factors. It is shown, that in a deterministic version, the model is equivalent to the Lorenz\ud system of differential equations. With reasonable parameter values the model exhibits chaotic\ud behaviour. It successfully emulates certain properties of interest rates including regime switching\ud and behaviour of a business cycle nature. Pricing and term structure issues are discussed.\ud Standard PCA techniques used to estimate HJM type models are observed to be equivalent to\ud dimensional estimates commonly applied to 'spatial data' in non-linear systems analysis. An\ud empirical investigation uncovers surprising structure consistent with the existence of a low\ud dimensional attractor. Issues of control of the chaotic system with reference to the underlying\ud economic model are discussed.\ud A heuristic approach is made to estimating the three factor model. Exploiting properties of the\ud term structure, the existence of noise, and the geometry of the system allows a variety of\ud methods for uncovering the parameters of the model. A better approach is found in the\ud application of the Kalman filter to the estimation problem. Lack of explicit solutions motivates an\ud investigation into the use of approximated forms for the term structure. The traditional Kalman\ud filter is seen to be unstable when applied to the chaotic three factor model. A stable variant, from\ud the class known as 'square-root' filters, is adopted. A new method is created for finding the\ud analytical derivatives of the log-likelihood function such that it is consistent with the 'square-root'\ud filter. Estimates for the empirical estimation of the models developed earlier in the thesis are\ud given.\ud It is concluded that there is much scope for expanding the literature within the new class of\ud models proposed. The particular three factor model developed has been shown to have realistic\ud properties and be amenable to bond and contingent claim pricing. The chaotic nature of the\ud model, underpinned by an economic derivation, opens up new methods for authorities to\ud control/stabilise the economy. An analysis of the underlying dynamical structure of UK money\ud market rates is consistent with a low dimensional deterministic driving force. Heuristic methods\ud employed to estimate the parameters of the model allow for an insight into exploiting the\ud geometry of the system. Application of the Kalman filter to estimation of non-linear models is\ud found to be problematic due to the linearisations/approximations that are necessary.\ud An outline of areas for future research is given, providing ideas for extending the economic\ud formulation, further investigating control of chaotic interest rate systems, testing empirical data\ud for evidence of chaotic invariants and methods for quantifying and improving the Kalman filtering\ud procedures for better handling non-linear models.
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • BLANCHARD OJ AND FISCHER S (1990). Lectures on Macroeconomics. Cambridge University Press: Cambridge.
    • BLANK SC (1991). 'Chaos' in futures markets? A nonlinear dynamical analysis. The Journal of Futures Markets 11: 711-728.
    • BLENMAN LP, CANTRELL RS, FENNELL RE, PARKER DF, RENEKE JA, WANG LFS AND WOMER NK (1995). An alternative approach to stochastic calculus for economic and financial models. Journal of Economic Dynamics and Control 19: 553-568.
    • BODIE Z, KANE A AND MARCUS AJ (1989). Investments. Irwin: Homewood.
    • BOLLERSLEV T, CHOU RY AND KRONER KF (1992). ARCH modelling in finance: a review of theory and empirical evidence. Journal of Econometrics 52: 5-59.
    • BOROWSKI EJ AND BORWEIN JM (1989). Dictionary of Mathematics. Harper Collins.
    • BOX GEP JENKINS GM AND REINSEL GC (1994). Time Series Analysis: Forecasting and Control, 3rd Ed. Prentice Hall: Englewood Cliffs.
    • BRANSON WH (1989). Macroeconomic Theory and Policy, 3rd ed. Harper & Row: New York.
    • BRENNAN MJ AND SCHWARTZ ES (1979). A continuous time approach to the pricing of bonds. Journal of Banking and Finance 3: 133-155.
    • BRENNAN MJ AND SCHWARTZ ES (1980). Analysing convertible bonds. Journal of Financial and Quantitative Analysis 15: 907-929.
    • BRENNAN MJ AND SCHWARTZ ES (1982). An equilibrium model of bond pricing and a test of market efficiency. Journal of Financial and Quantitative Analysis 18: 301- 329.
    • BROCK WA (1986). Distinguishing random and deterministic systems: abridged version. In: GRANDMONT J-M (ED). Nonlinear Economic Dynamics: 168-195. Academic Press: Orlando.
    • BROCK WA (1986). Is the business cycle characterised by deterministic chaos? In: GRANDMONT J (ED). Nonlinear Economic Dynamics. Academic Press: Orlando.
    • BROCK WA (1988). Nonlinearity and complex dynamics in economics and finance. In: ANDERSON PW, ARROW KJ AND PINES D (EDS). The Economy as an Evolving Complex System. Addison Wesley: Reading.
    • BROCK WA (1993). Pathways to randomness in the economy: emergent nonlinearity and chaos in economics and finance. Estudios Econ6micos 8: 3-56.
    • BROCK WA (1996). Asset Price Behaviour in Complex Environments. Research Paper, Social Systems Research Institute, University of Wisconsin Madison.
    • BROCK WA AND BAEK EG (1991). Some theory of statistical inference for nonlinear science. Review of Economic Studies 58: 697-716.
    • BROCK WA AND BAEK EG (1992). A nonparametric test for independence of a multivariate time series. Statistica Sinica 2: 137-156.
    • BROCK WA AND DE LIMA PJF (1996). Nonlinear time series, complexity theory, and finance. In: MADDALA GS AND RAO CR (EDS). Handbook of Statistics 14: 317-361. Elsevier Science B. V.
    • BROCK WA AND HOMMES CH (1995). Rational routes to randomness. Research Paper, Social Systems Research Institute, University of Wisconsin-Madison.
    • BROCK WA AND HOMMES CH (1997). Models of complexity in economics and finance. Research Paper, Social Systems Research Institute, University of Wisconsin Madison.
    • BROCK WA AND KLEIDON AW (1992). Periodic market closure and trading volume - a model of intraday bids and asks. Journal of Economic Dynamics and Control 16: 451.
    • BROCK WA AND LEBARON BD (1996). A dynamic structural model for stock return volatility and trading volume. Review of Economics and Statistics 78: 94-110.
    • BROCK WA AND MALLIARIS AG (1989). Differential Equations, Stability and Chaos in Dynamic Economics. North Holland: Oxford.
    • BROCK WA AND POTTER SM (1993). Nonlinear time series and macroeconometrics. In: RAO CR (ED). Handbook of Statistics 11. Elsevier Science.
    • BROCK WA AND SAYERS CL (1988). Is the business cycle characterized by deterministic chaos? Journal of Monetary Economics 22: 71-90.
    • BROCK WA, DECHERT WD, LEBARON B AND SCHEINKMAN JA (1996). A test for independence based on the correlation dimension. Econometric Reviews 15: 197- 235.
    • BROCK WA, HSIEH DA AND LEBARON B (1991). Nonlinear Dynamics, Chaos and Instability: Statistical Theory and Economic Evidence. MIT Press: London.
    • BROCK WA, LAKONISHOK J AND LEBARON B (1992). Simple technical trading rules and the stochastic properties of stock returns. The Journal of Finance 47.
    • BROOMHEAD DS AND KING GP (1986). Extracting qualitative dynamics from experimental data. Physica D 20: 217-236.
    • BROWN R AND CHUA LO (1996). Clarifying chaos: examples and counterexamples. International Journal of Bifurcation and Chaos 6: 219:249.
    • BROWN R, RULKOV N AND TUFILLARO N (1994). The effects of additive noise and drift in the dynamics of the driving on chaotic synchronisation. Unpublished Paper, Institute for Nonlinear Science, University of California, San Diego and Centre for Nonlinear Studies, Los Alamos National Laboratory.
    • BROWN RH AND SCHAEFER SM (1994). The term structure of real interest rates and the Cox, Ingersoll and Ross model. Journal of Financial Economics 35: 3-42.
    • BUCY RS AND JOSEPH PD (1968) Filtering for Stochastic Processes, with Applications to Guidance. Wiley, New York,
    • CAGINALP G AND BALENOVICH D (1994). Market oscillations induced by the competition between value-based and trend-based investment strategies. Applied Mathematical Finance 1: 129-164.
    • CANABARRO E (1993). Comparing the dynamic accuracy of yield-curve-based interest rate contingent claim pricing models. Journal of Financial Engineering 2: 365-401.
    • CAO CQ AND TSAY RS (1992). Non-linear time series analysis of stock volatilities. Journal of Applied Econometrics 7: 165-185.
    • CARROLL RJ, RUPPERT D AND STEFANSKI LA (1995). Measurement Error in Nonlinear Models. Chapman & Hall: London.
    • CHAPMAN DA, PEARSON ND (1998). Is the short rate drift actually nonlinear? Working Paper, Graduate School of Business, University of Texas. Available from http://www.bus.utexas.edu/-chapmand/cp.html.
    • CHAPMAN DA, LONG JB AND PEARSON ND (1998). Using proxies for the short rate: When are three months like an instant? Working paper, Finance Department, Graduate School of Business, University of Texas. Available from http://www.bus.utexas.edut-chapmand/c1p.html.
    • CHAN KC, KAROLYI C, LONGSTAFF GA AND SANDERS FA (1992). The volatility of short term interest rates: an empirical comparison of alternative models of the term structure of interest rates. Journal of Finance 47: 209-1227.
    • CHEN L (1996). Stochastic mean and stochastic volatility - a three-factor model of the term structure of interest rates and its implications in derivatives and pricing management. Financial Markets, Institutions and Instruments 5: 1-88.
    • CHEN P (1993). Searching for economic chaos: a challenge to econometric practice and nonlinear tests. In: DAY R AND CHEN P (EDS). Nonlinear Dynamics and Evolutionary Economics. Oxford University Press: Oxford.
    • CHEN S AND BILLINGS A (1992). Neural networks for nonlinear dynamic systems modelling and identification. International Journal of Control 56: 319-346.
    • CHIANG AC (1984). Fundamental Methods of Mathematical Economics, 3rd Ed. McGraw-Hill: Singapore.
    • CHICHILNISKY G, HEAL G AND LIN Y (1995). Chaotic price dynamics, increasing returns and the Phillips curve. Journal of Economic Behaviour and Organisation 27: 279-291.
    • CHOI H (1995). Goodwin's growth cycle and the efficiency wage hypothesis. Journal of Economic Behaviour and Organisation 27: 223-35.
    • COPELAND TE AND WESTON JP (1988). Financial Theory and Corporate Policy. Addison-Wesley: Reading.
    • COULLET P, ELPHICK C AND REPAUX D (1987). Nature of spatial chaos. Physical Review Letters 58: 431-435.
    • Cox DR AND MILLER HD (1995). The Theory of Stochastic Processes. Chapman & Hall: London.
    • Cox JC, INGERSOLL JE AND ROSS SA (1980). An analysis of variable rate loans contracts. The Journal of Finance 35: 389-403.
    • COX JC, INGERSOLL JE AND ROSS SA (1985a). An intertemporal general equilibrium model of asset prices. Econometrica 53: 363-384.
    • COX JC, INGERSOLL JE AND ROSS SA (1985b). A theory of the term structure of interest rates. Econometrica 53: 385-407.
    • CREEDY J AND MARTIN VL (EDS) (1994). Chaos and Non-linear Models in Economics. Edward Elgar: Aldershot.
    • DAY RH (1992). Complex economic dynamics: obvious in history, generic in theory, elusive in data. Journal of Applied Econometrics 7: S9-S23.
    • DAY RH (1994). Complex Econotnic Dynamics. MIT Press: Cambridge.
    • DAY RH AND CHEN P (1993). Nonlinear Dynamics and Evolutionary Economics. Oxford University Press: Oxford.
    • DAY RH AND SHAFER W (1992). Keynesian chaos. In: BENHABIB J (ED). Cycles and Chaos in Equilibrium. Princeton University Press: Princeton.
    • DE GRAWE P, DEWACHTER H AND EMBRECHTS M (1994). Exchange Rate Theory: Chaotic Models of Foreign Exchange Markets. Blackwell: Oxford.
    • DE JONG P AND SHEPARD N (1995). The simulation smoother for time series models. Biometrika 82: 339-350.
    • DECHERT WD AND GENCAY R (1992). Lyapunov exponents as a nonparametric diagnostic for stability analysis. Journal of Applied Econometrics 7: S41-560.
    • DEISSLER RJ (1987). Spatially growing waves, intermittency, and convective chaos in an open-flow system. Physica D 25: 233-260.
    • DERNBURG TF AND DERNBURG JD (1969). Macroeconomic Analysis: An Introduction to Comparative Statics and Dynamics. Addison-Wesley: Reading.
    • DEVANEY RL (1989). An Introduction to Chaotic Dynamical Systems, 2nd Ed. Addison-Wesley: Reading.
    • DEWSON T AND IRVING AD (1996). Mixed order response function estimation from multi-input non-linear systems. Physica D 94: 19-35.
    • DORNBUSCH R AND FISCHER S (1990). Macroeconomics, 5th Ed. McGraw-Hill: Singapore.
    • DOTHAN LU (1978). On the term structure of interest rates. Journal of Financial Economics 6: 59-69.
    • DOTHAN MU (1990). Prices in Financial Markets. Oxford University Press: Oxford.
    • DUFFIE D (1992). Dynamic Asset Pricing Theory. Princeton University Press: Princeton.
    • DUFFIE D AND KAN R (1994). Multi-factor term structure models. Philosophical Transactions of the Royal Society of London A 347: 577-586.
    • DUFFIE D AND KAN R (1996). A yield factor model of interest rates. Mathematical Finance 6: 379-406.
    • ECKMANN J-P AND RUELLE D (1985). Ergodic theory of chaos and strange attractors. Reviews of Modern Physics 57: 617-656.
    • EDELHART M AND NATH S (1988). The Brady Book of Turbo Pascal. Prentice Hall: New York.
    • EDGAR GA (1992). Measure, Topology, and Fractal Geometry. Springer-Verlag: New York.
    • ELTON EJ AND GRUBER MJ (1991). Modern Portfolio Theory and Investment Analysis. Wiley: New York.
    • ENGLE RF (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica 50: 987-1007.
    • EVANS GA (1995). Practical Numerical Analysis. Wiley: Chichester.
    • FARMER REA (1986). Deficits and cycles. In: GRANDMONT J-M (ED). Nonlinear Economic Dynamics: 77-88. Academic Press: Orlando.
    • FRANKEL JA (1993). On Exchange Rates. MIT Press: Cambridge.
    • FRAZER AM (1996). Chaos and detection. Physical Review E 53: 4514: 4523.
    • FROYLAND G, JUDD K AND MEES Al (1995). Estimation of Lyapunov exponents of dynamical systems using a spatial average. Physical Review E 51: 2844-2855.
    • GEKAY R (1996). A statistical framework for testing chaotic dynamics via Lyapunov exponents. Physica D 89: 261-266.
    • GILMORE CG (1993). A new test for chaos. Journal of Economic Behaviour and Organization 22: 209-237.
    • GOLUB G E AND VAN LOAN CF (1983). Matrix Computations. North Oxford Academic: Oxford.
    • GOmEz V (undated). Estimation and signal extraction for finite nonstationary series with the Kalman filter. Research Paper, Available from: Victor GOmez, Ministerio de Economia y Hacienda, Paseo de la Casteliana 162, 28046 Madrid, Spain.
    • GOODWIN RM (1990). Chaotic Economic Regimes. Clarendon: Oxford.
    • GOODWIN RM AND PACINI PM (1992). Nonlinear economic dynamics and chaos: an introduction. In: VERCELLI A AND DIMITRI N (EDS). Macroeconomics: A Survey of Research Strategies: 236-291. Oxford University Press: Oxford.
    • GOURIEROUX C AND MONFORT A (1996). Simulation-Based Econometric Methods. Oxford University Press: Oxford.
    • GRANDMONT J-M (1986). Stabilising competitive business cycles. In: GRANDMONT M (ED). Nonlinear Economic Dynamics: 57-76. Academic Press: Orlando.
    • GRANGER CW AND TERASVIRTA T (1993). Modelling Nonlinear Economic Relationships. Oxford University Press: Oxford.
    • GRANGER CWJ (1968). Some aspects of the Random Walk Model of stock market prices. International Economic Review 9: 253-259.
    • GRANGER CWJ (1992). Forecasting stock market prices: lessons for forecasters. International Journal of Forecasting 8: 3-13. GRANGER CWJ (ED) (1990). Modelling Economic Series, Readings in Econometric Methodology. Clarendon: Oxford. GRANGER CWJ (ED) (1991). Long Run Economic Relationships, Readings in Coitztergration. Oxford University Press: Oxford. GRANGER CWJ AND NEWBOLD P (1986). Forecasting Economic Time Series, 2nd Ed. Academic Press: Orlando.
    • GRASSBERGER P AND PROCACCIA 1(1983). Measuring the strangeness of the strange attractor. Physica D 9: 189-208.
    • GRENFELL BT, KLEGZKowsKi A, ELLNER SP AND BOLKER BM (1994). Measles as a case study in nonlinear forecasting and chaos. Philosophical Transactions of the Royal Society of London A 348: 515-530.
    • GREWAL MS AND ANDREWS AP (1993). Kalman Filtering: Theory and Practice. Prentice Hall: Englewood Cliffs.
    • GU M (1993). An empirical examination of the deterministic component in stock price volatility. Journal of Economic Behaviour and Organisation 22: 239-252.
    • Gu M (1995). Market mediating behaviour: an economic analysis of security exchange specialists. Journal of Economic Behaviour and Organisation 27: 237-56.
    • GUILLAUME DM, PICTET OV, MOLLER UA AND DACOROGNA MM (1995). Unveiling non-linearities through time scale transformations. Research Paper, Olsen Associates, Available from http:\\www.olsen.ch\
    • GUJARATI DN (1988). Basic Econometrics, 2nd Ed. McGraw-Hill: Singapore.
    • HAKKIO CS AND LEIDERMAN L (1986). Intertemporal asset pricing and the term structure of exchange rates and interest rates - the eurocurrency market. European Economic Review 30: 325-344.
    • HAMILTON JD (1994). Time Series Analysis. Princeton University Press: Princeton.
    • HARVEY AC (1989). Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge University Press: Cambridge.
    • HARVEY AC AND STOCK JH (1993). Estimation, smoothing, interpolation, and distribution for structural time-series models in continuous time. In: PHILLIPS PCB (ED). Modern Methods and Applications of Econometrics. Blackwell: Oxford.
    • HE X AND LAPEDES A (1994). Nonlinear modelling and prediction by successive approximation using radial basis functions. Physica D 70: 289-301.
    • YAO Q AND TONG H (1994). On prediction and chaos in stochastic systems. Philosophical Transactions of the Royal Society of London A 348: 357-369.
    • ZAPATERO F (1995). Equilibrium asset prices and exchange rates. Journal of Economic Dynamics and Control 19: 787-811.
    • ZASLAVSKY GM, SAGDEEV RZ, USIKOV DA AND CHERNIKOV AA (1992). Weak Chaos and Quasi-Regular Patterns. Cambridge University Press: Cambridge.
    • ZHANG X, HUTCHINSON J (1994). Practical issues in nonlinear time series prediction. In: WEIGEND AS AND GERSHENFELD NA (EDS). Time Series Prediction: Forecasting the Future and Understanding the Past. Addison-Wesley: Reading.
  • No related research data.
  • No similar publications.

Share - Bookmark

Cite this article