IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/24844.html
   My bibliography  Save this paper

Simulation of interest rate options using ARCH

Author

Listed:
  • Bianchi, Carlo
  • Calzolari, Giorgio
  • Sterbenz, Frederic P.

Abstract

The autoregressive conditional heteroskedasticity (ARCH) estimation procedure provides a specification of the error terms as well as estimates of the coefficients. A simple interest rate equation is estimated using least squares and also using ARCH. Then the stochastic simulation methodology is extended to the ARCH process and Treasury Bond call options are evaluated. Interestingly when ARCH is compared to least squares it is found that the difference in coefficients estimates has a small effect, while the different simulation procedures have a large effect on the value of Treasury Bond call options.

Suggested Citation

  • Bianchi, Carlo & Calzolari, Giorgio & Sterbenz, Frederic P., 1991. "Simulation of interest rate options using ARCH," MPRA Paper 24844, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:24844
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/24844/1/MPRA_paper_24844.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Calzolari, Giorgio, 1979. "Antithetic variates to estimate the simulation bias in non-linear models," Economics Letters, Elsevier, vol. 4(4), pages 323-328.
    2. Pagan, Adrian R. & Schwert, G. William, 1990. "Alternative models for conditional stock volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 267-290.
    3. Ball, Clifford A, 1988. " Estimation Bias Induced by Discrete Security Prices," Journal of Finance, American Finance Association, vol. 43(4), pages 841-865, September.
    4. Ross, Stephen A, 1978. "A Simple Approach to the Valuation of Risky Streams," The Journal of Business, University of Chicago Press, vol. 51(3), pages 453-475, July.
    5. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    6. Hendry, David F., 1984. "Monte carlo experimentation in econometrics," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 16, pages 937-976, Elsevier.
    7. Jamshidian, Farshid, 1989. " An Exact Bond Option Formula," Journal of Finance, American Finance Association, vol. 44(1), pages 205-209, March.
    8. Sterbenz, Frederic P & Calzolari, Giorgio, 1990. "Alternative Specifications of the Error Process in the Stochastic Simulation of Econometric Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(2), pages 137-150, April-Jun.
    9. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-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. Fiorentini, Gabriele & Calzolari, Giorgio & Panattoni, Lorenzo, 1996. "Analytic Derivatives and the Computation of GARCH Estimates," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(4), pages 399-417, July-Aug..
    2. Calzolari, Giorgio & Fiorentini, Gabriele, 1994. "Conditional heteroskedasticity in nonlinear simultaneous equations," MPRA Paper 24428, University Library of Munich, Germany.
    3. Calzolari, Giorgio & Fiorentini, Gabriele & Panattoni, Lorenzo, 1993. "Alternative estimators of the covariance matrix in GARCH models," MPRA Paper 24433, University Library of Munich, Germany.

    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. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    2. repec:dau:papers:123456789/5374 is not listed on IDEAS
    3. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    4. repec:uts:finphd:40 is not listed on IDEAS
    5. Samuel Chege Maina, 2011. "Credit Risk Modelling in Markovian HJM Term Structure Class of Models with Stochastic Volatility," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2011.
    6. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742, Elsevier.
    7. Boero, G. & Torricelli, C., 1996. "A comparative evaluation of alternative models of the term structure of interest rates," European Journal of Operational Research, Elsevier, vol. 93(1), pages 205-223, August.
    8. Carl Chiarella & Christina Nikitopoulos Sklibosios & Erik Schlogl, 2007. "A Control Variate Method for Monte Carlo Simulations of Heath-Jarrow-Morton Models with Jumps," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(5), pages 365-399.
    9. Kevin John Fergusson, 2018. "Less-Expensive Pricing and Hedging of Extreme-Maturity Interest Rate Derivatives and Equity Index Options Under the Real-World Measure," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 3-2018.
    10. Mondher Bellalah, 2009. "Derivatives, Risk Management & Value," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 7175, January.
    11. Munk, Claus, 2015. "Financial Asset Pricing Theory," OUP Catalogue, Oxford University Press, number 9780198716457.
    12. Giorgio Calzolari & F. Di Iorio & G. Fiorentini, 1999. "Indirect Estimation of Just-Identified Models with Control Variates," Econometrics Working Papers Archive quaderno46, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
    13. Ben-Ameur, Hatem & Breton, Michele & Karoui, Lotfi & L'Ecuyer, Pierre, 2007. "A dynamic programming approach for pricing options embedded in bonds," Journal of Economic Dynamics and Control, Elsevier, vol. 31(7), pages 2212-2233, July.
    14. Fergusson, Kevin, 2020. "Less-Expensive Valuation And Reserving Of Long-Dated Variable Annuities When Interest Rates And Mortality Rates Are Stochastic," ASTIN Bulletin, Cambridge University Press, vol. 50(2), pages 381-417, May.
    15. Christina Nikitopoulos-Sklibosios, 2005. "A Class of Markovian Models for the Term Structure of Interest Rates Under Jump-Diffusions," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 6, July-Dece.
    16. Gibson, Rajna & Lhabitant, Francois-Serge & Talay, Denis, 2010. "Modeling the Term Structure of Interest Rates: A Review of the Literature," Foundations and Trends(R) in Finance, now publishers, vol. 5(1–2), pages 1-156, December.
    17. Hatem Ben-Ameur & Michèle Breton, 2004. "A Dynamic Programming Approach for Pricing Options Embedded in Bonds," Computing in Economics and Finance 2004 237, Society for Computational Economics.
    18. Erik Schlogl & Lutz Schlogl, 2000. "A square root interest rate model fitting discrete initial term structure data," Applied Mathematical Finance, Taylor & Francis Journals, vol. 7(3), pages 183-209.
    19. Constantin Mellios, 2001. "Valuation of Interest Rate Options in a Two-Factor Model of the Term Structure of Interest Rate," Working Papers 2001-1, Laboratoire Orléanais de Gestion - université d'Orléans.
    20. Samuel Chege Maina, 2011. "Credit Risk Modelling in Markovian HJM Term Structure Class of Models with Stochastic Volatility," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 5, July-Dece.
    21. Gajda, Jan B. & Markowski, Aleksander, 1998. "Model Evaluation Using Stochastic Simulations: The Case of the Econometric Model KOSMOS," Working Papers 61, National Institute of Economic Research.
    22. Blöchlinger, Andreas, 2021. "Interest rate risk in the banking book: A closed-form solution for non-maturity deposits," Journal of Banking & Finance, Elsevier, vol. 125(C).

    More about this item

    Keywords

    ARCH model; simulation; interest rate; Treasury bond call options;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • 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:pra:mprapa:24844. 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: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.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.