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Interest rate option pricing and volatility forecasting: An application to Brazil

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  • Takami, Marcelo Yoshio
  • Tabak, Benjamin Miranda

Abstract

Assessing the markets perception of future interest and inflation rate volatility is of crucial importance to assess the evolution of expectations in an inflation targeting framework. This article aims to evaluate the information content of implied volatilities extracted from a Brazilian interest-rate call option. We compared the predictive performance of three different approaches: one using the traditional [Black F. The pricing of commodity contracts. J Financ Econ 1976;3:167–79] method, another one using the extended-Vasicek model, and in the third approach, we use a GARCH(2,1) model. The empirical evidence was more favorable to the extended-Vasicek method. Moreover, extended-Vasicek’s implied volatilities could predict around 33% (adjusted R2) of the variations in realized volatility. Further research could test for the predictive content of long memory options such as those suggested in Wang et al. [Wang X-T, Qiu W-Y, Ren F-Y. Option pricing of fractional version of the Black–Scholes model with Hurst exponent H being in 13,12. Chaos, Solitons & Fractals 2001;12:599–608; Wang X-T, Ren F-Y, Liang X-Q. A fractional version of the Merton model. Chaos, Solitons & Fractals 2003;15:455–63].

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  • Takami, Marcelo Yoshio & Tabak, Benjamin Miranda, 2008. "Interest rate option pricing and volatility forecasting: An application to Brazil," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 755-763.
    • Handle: RePEc:eee:chsofr:v:38:y:2008:i:3:p:755-763
    DOI: 10.1016/j.chaos.2007.01.038
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    1. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    2. Cajueiro, Daniel O. & Tabak, Benjamin M., 2007. "Long-range dependence and multifractality in the term structure of LIBOR interest rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 373(C), pages 603-614.
    3. Monika Piazzesi, 2005. "Bond Yields and the Federal Reserve," Journal of Political Economy, University of Chicago Press, vol. 113(2), pages 311-344, April.
    4. 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.
    5. 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.
    6. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    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. Canina, Linda & Figlewski, Stephen, 1993. "The Informational Content of Implied Volatility," Review of Financial Studies, Society for Financial Studies, vol. 6(3), pages 659-681.
    9. Tan, Abby, 2006. "Long-memory volatility in derivative hedging," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(2), pages 689-696.
    10. Hull, John & White, Alan, 1993. "One-Factor Interest-Rate Models and the Valuation of Interest-Rate Derivative Securities," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 28(2), pages 235-254, June.
    11. Sandro Canesso de Andrade & Benjamin Miranda Tabak, 2001. "Is it Worth Tracking Dollar/Real Implied Volatility?," Working Papers Series 15, Central Bank of Brazil, Research Department.
    12. Tabak, Benjamin M. & Cajueiro, Daniel O., 2005. "The long-range dependence behavior of the term structure of interest rates in Japan," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 350(2), pages 418-426.
    13. Cajueiro, Daniel O. & Tabak, Benjamin M., 2007. "Long-range dependence and market structure," Chaos, Solitons & Fractals, Elsevier, vol. 31(4), pages 995-1000.
    14. 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.
    15. Dothan, L. Uri, 1978. "On the term structure of interest rates," Journal of Financial Economics, Elsevier, vol. 6(1), pages 59-69, March.
    16. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "An Intertemporal General Equilibrium Model of Asset Prices," Econometrica, Econometric Society, vol. 53(2), pages 363-384, March.
    17. Heynen, Ronald & Kemna, Angelien & Vorst, Ton, 1994. "Analysis of the Term Structure of Implied Volatilities," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 29(1), pages 31-56, March.
    18. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    19. Lima, Eduardo Jose Araújo & Tabak, Benjamin Miranda, 2007. "Testing for inefficiency in emerging markets exchange rates," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 617-622.
    20. Garman, Mark B. & Kohlhagen, Steven W., 1983. "Foreign currency option values," Journal of International Money and Finance, Elsevier, vol. 2(3), pages 231-237, December.
    21. Harvey, David & Leybourne, Stephen & Newbold, Paul, 1997. "Testing the equality of prediction mean squared errors," International Journal of Forecasting, Elsevier, vol. 13(2), pages 281-291, June.
    22. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
    23. Brennan, Michael J. & Schwartz, Eduardo S., 1978. "Finite Difference Methods and Jump Processes Arising in the Pricing of Contingent Claims: A Synthesis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 13(3), pages 461-474, September.
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    1. Jonathan A. Batten & Cetin Ciner & Brian M. Lucey & Peter G. Szilagyi, 2013. "The structure of gold and silver spread returns," Quantitative Finance, Taylor & Francis Journals, vol. 13(4), pages 561-570, March.

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