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Simulation of interest rate options using ARCH

Author

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  • 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
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    File URL: https://mpra.ub.uni-muenchen.de/24844/1/MPRA_paper_24844.pdf
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    References listed on IDEAS

    as
    1. Pagan, Adrian R. & Schwert, G. William, 1990. "Alternative models for conditional stock volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 267-290.
    2. Calzolari, Giorgio, 1979. "Antithetic variates to estimate the simulation bias in non-linear models," Economics Letters, Elsevier, vol. 4(4), pages 323-328.
    3. Jamshidian, Farshid, 1989. " An Exact Bond Option Formula," Journal of Finance, American Finance Association, vol. 44(1), pages 205-209, March.
    4. 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.
    5. Ball, Clifford A, 1988. " Estimation Bias Induced by Discrete Security Prices," Journal of Finance, American Finance Association, vol. 43(4), pages 841-865, September.
    6. 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.
    7. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    8. 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.
    9. 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.
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    Citations

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    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.

    More about this item

    Keywords

    ARCH model; simulation; interest rate; Treasury bond call options;

    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

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