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The Probability Density Function of Interest Rates Implied in the Price of Options

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  • Fornari, F.
  • Violi, R.

Abstract

The paper contributes to the stochastic volatility literature by developing simulation schemes for the conditional distributions of the price of long term bonds and their variability based on non-standard distributional assumptions and volatility concepts; it illustrates the potential value of the information contained in the prices of options on long and short term lira interest rate futures for the conduct of monetary policy in Italy, at times when significant regime shifts have occured.

Suggested Citation

  • Fornari, F. & Violi, R., 1998. "The Probability Density Function of Interest Rates Implied in the Price of Options," Papers 339, Banca Italia - Servizio di Studi.
    • Handle: RePEc:fth:banita:339
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    References listed on IDEAS

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    1. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
    2. Soderlind, Paul & Svensson, Lars, 1997. "New techniques to extract market expectations from financial instruments," Journal of Monetary Economics, Elsevier, vol. 40(2), pages 383-429, October.
    3. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    4. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    5. Fabio Fornari & Antonio Mele, 1997. "Weak convergence and distributional assumptions for a general class of nonliner arch models," Econometric Reviews, Taylor & Francis Journals, vol. 16(2), pages 205-227.
    6. Malz, Allan M., 1996. "Using option prices to estimate realignment probabilities in the European Monetary System: the case of sterling-mark," Journal of International Money and Finance, Elsevier, vol. 15(5), pages 717-748, October.
    7. Engle, Robert F. & Mustafa, Chowdhury, 1992. "Implied ARCH models from options prices," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 289-311.
    8. David K. Backus & Stanley E. Zin, 1994. "Reverse Engineering the Yield Curve," NBER Working Papers 4676, National Bureau of Economic Research, Inc.
    9. Melick, William R. & Thomas, Charles P., 1997. "Recovering an Asset's Implied PDF from Option Prices: An Application to Crude Oil during the Gulf Crisis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 32(1), pages 91-115, March.
    10. Campa, Jose Manuel & Chang, P H Kevin, 1995. "Testing the Expectations Hypothesis on the Term Structure of Volatilities in Foreign Exchange Options," Journal of Finance, American Finance Association, vol. 50(2), pages 529-547, June.
    11. Bossaerts, Peter & Hillion, Pierre, 1997. "Local parametric analysis of hedging in discrete time," Journal of Econometrics, Elsevier, vol. 81(1), pages 243-272, November.
    12. 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.
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    Cited by:

    1. Martin Mandler, 2002. "Extracting Market Expectations from Option Prices: Two Case Studies in Market Perceptions of the ECB's Monetary Policy 1999/2000," Swiss Journal of Economics and Statistics (SJES), Swiss Society of Economics and Statistics (SSES), vol. 138(II), pages 165-189, June.
    2. Siviero, S. & Terlizzese, D. & Visco, I., 1999. "Are Model-Based Inflation Forecasts Used in Monetary Policymaking? A Case Study," Papers 357, Banca Italia - Servizio di Studi.
    3. Marcello Pericoli, 2005. "Can option smiles forecast changes in interest rates? An application to the US, the UK and the euro area," Temi di discussione (Economic working papers) 545, Bank of Italy, Economic Research and International Relations Area.

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    More about this item

    Keywords

    STOCHASTIC MODELS ; STATISTICAL ANALYSIS ; INTEREST RATE ; FINANCIAL MARKET;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects

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