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Multifactor and analytical valuation of treasury bond futures with an embedded quality option

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  • João Pedro Vidal Nunes
  • Luís Alberto Ferreira De Oliveira

Abstract

A closed‐form pricing solution is proposed for the quality option embedded in Treasury bond futures contracts, under a multifactor and D. Heath, R. Jarrow, and A. Morton (1992) Gaussian framework. Such an analytical solution can be obtained through a conditioning approximation, in the sense of M. Curran (1994) and L. Rogers and Z. Shi (1995), or via a rank 1 approximation, following A. Brace and M. Musiela (1994). Monte Carlo simulations show that both approximations are extremely accurate and easy to calculate. Application of the proposed pricing model to the EUREX market from January 2000 through May 2004, yields an excellent fit and an insignificant estimate of the quality option magnitude. On average, this delivery option accounts for only of the futures prices. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:275–303, 2007

Suggested Citation

  • João Pedro Vidal Nunes & Luís Alberto Ferreira De Oliveira, 2007. "Multifactor and analytical valuation of treasury bond futures with an embedded quality option," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 27(3), pages 275-303, March.
  • Handle: RePEc:wly:jfutmk:v:27:y:2007:i:3:p:275-303
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    1. Simon Benninga & Michael Smirlock, 1985. "An empirical analysis of the delivery option, marking to market, and the pricing of treasury bond futures," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 5(3), pages 361-374, September.
    2. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    3. Tomas Björk & Bent Jesper Christensen, 1999. "Interest Rate Dynamics and Consistent Forward Rate Curves," Mathematical Finance, Wiley Blackwell, vol. 9(4), pages 323-348.
    4. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(04), pages 627-627, November.
    5. Klaus Sandmann & J. Aase Nielsen, 2002. "Pricing of Asian exchange rate options under stochastic interest rates as a sum of options," Finance and Stochastics, Springer, vol. 6(3), pages 355-370.
    6. Theodore M. Barnhill & William E. Seale, 1988. "Optimal exercise of the switching option in treasury bond arbitrages," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 8(5), pages 517-532, October.
    7. Peter Ritchken & L. Sankarasubramanian, 1992. "Pricing the Quality Option In Treasury Bond Futures," Mathematical Finance, Wiley Blackwell, vol. 2(3), pages 197-214.
    8. Ritchken, Peter & Sankarasubramanian, L, 1995. "A Multifactor Model of the Quality Option in Treasury Futures Contracts," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 18(3), pages 261-279, Fall.
    9. McCulloch, J Huston, 1971. "Measuring the Term Structure of Interest Rates," The Journal of Business, University of Chicago Press, vol. 44(1), pages 19-31, January.
    10. Heath, David & Jarrow, Robert & Morton, Andrew, 1990. "Bond Pricing and the Term Structure of Interest Rates: A Discrete Time Approximation," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 25(04), pages 419-440, December.
    11. Gay, Gerald D. & Manaster, Steven, 1984. "The quality option implicit in futures contracts," Journal of Financial Economics, Elsevier, vol. 13(3), pages 353-370, September.
    12. Livingston, Miles, 1987. "The Delivery Option on Forward Contracts," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(01), pages 79-87, March.
    13. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters,in: Theory Of Valuation, chapter 5, pages 129-164 World Scientific Publishing Co. Pte. Ltd..
    14. D. P. Kennedy, 1994. "The Term Structure Of Interest Rates As A Gaussian Random Field," Mathematical Finance, Wiley Blackwell, vol. 4(3), pages 247-258.
    15. Duan, Jin-Chuan & Simonato, Jean-Guy, 1999. "Estimating and Testing Exponential-Affine Term Structure Models by Kalman Filter," Review of Quantitative Finance and Accounting, Springer, vol. 13(2), pages 111-135, September.
    16. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    17. Boyle, Phelim P, 1989. " The Quality Option and Timing Option in Futures Contracts," Journal of Finance, American Finance Association, vol. 44(1), pages 101-113, March.
    18. Don M. Chance & Michael L. Hemler, 1993. "The impact of delivery options on futures prices: A survey," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 13(2), pages 127-155, April.
    19. Alan Brace & Marek Musiela, 1994. "A Multifactor Gauss Markov Implementation Of Heath, Jarrow, And Morton," Mathematical Finance, Wiley Blackwell, vol. 4(3), pages 259-283.
    20. Hegde, Shantaram P., 1988. "An empirical analysis of implicit delivery options in the treasury bond futures contract," Journal of Banking & Finance, Elsevier, vol. 12(3), pages 469-492, September.
    21. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305 World Scientific Publishing Co. Pte. Ltd..
    22. Peter Ritchken & L. Sankarasubramanian, 1995. "A Multifactor Model Of The Quality Option In Treasury Futures Contracts," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 18(3), pages 261-279, September.
    23. Cox, John C. & Ingersoll, Jonathan Jr. & Ross, Stephen A., 1981. "The relation between forward prices and futures prices," Journal of Financial Economics, Elsevier, vol. 9(4), pages 321-346, December.
    24. Nielsen, J. Aase & Sandmann, Klaus, 2003. "Pricing Bounds on Asian Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 38(02), pages 449-473, June.
    25. Nelson, Charles R & Siegel, Andrew F, 1987. "Parsimonious Modeling of Yield Curves," The Journal of Business, University of Chicago Press, vol. 60(4), pages 473-489, October.
    26. Margrabe, William, 1978. "The Value of an Option to Exchange One Asset for Another," Journal of Finance, American Finance Association, vol. 33(1), pages 177-186, March.
    27. Avi Bick, 1997. "Two Closed-Form Formulas for the Futures Price in the Presence of a Quality Option," Review of Finance, European Finance Association, vol. 1(1), pages 81-104.
    28. Hemler, Michael L, 1990. " The Quality Delivery Option in Treasury Bond Futures Contracts," Journal of Finance, American Finance Association, vol. 45(5), pages 1565-1586, December.
    29. 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.
    30. Alex Kane & Alan J. Marcus, 1986. "The quality option in the treasury bond futures market: An empirical assessment," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 6(2), pages 231-248, June.
    31. 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.
    32. Michael Curran, 1994. "Valuing Asian and Portfolio Options by Conditioning on the Geometric Mean Price," Management Science, INFORMS, vol. 40(12), pages 1705-1711, December.
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