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Interest rate options valuation under incomplete information

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  • Constantin Mellios

Abstract

This paper aims at examining the term structure of interest rates and European-type interest rate option prices in a partially observable economy. It extends the existing literature on incomplete information by developing a one-factor model which is consistent with the initial yield curve and by providing closed-form solutions for discount bonds and different kinds of options. The model of this paper encompasses Hull and White’s (1990). Moreover, through a numerical example, these two models are compared and the impact of incomplete information on option prices is analysed. Copyright Springer Science+Business Media, LLC 2007

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  • Constantin Mellios, 2007. "Interest rate options valuation under incomplete information," Annals of Operations Research, Springer, vol. 151(1), pages 99-117, April.
  • Handle: RePEc:spr:annopr:v:151:y:2007:i:1:p:99-117:10.1007/s10479-006-0128-2
    DOI: 10.1007/s10479-006-0128-2
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    1. Darrell Duffie & Chi-Fu Huang, 2005. "Implementing Arrow-Debreu Equilibria By Continuous Trading Of Few Long-Lived Securities," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 4, pages 97-127, World Scientific Publishing Co. Pte. Ltd..
    2. Dothan, Michael U & Feldman, David, 1986. "Equilibrium Interest Rates and Multiperiod Bonds in a Partially Observable Economy," Journal of Finance, American Finance Association, vol. 41(2), pages 369-382, June.
    3. Gennotte, Gerard, 1986. "Optimal Portfolio Choice under Incomplete Information," Journal of Finance, American Finance Association, vol. 41(3), pages 733-746, July.
    4. Jamshidian, Farshid, 1989. " An Exact Bond Option Formula," Journal of Finance, American Finance Association, vol. 44(1), pages 205-209, March.
    5. Tomas Björk & Bent Jesper Christensen, 1999. "Interest Rate Dynamics and Consistent Forward Rate Curves," Mathematical Finance, Wiley Blackwell, vol. 9(4), pages 323-348, October.
    6. Yihong Xia, 2001. "Learning about Predictability: The Effects of Parameter Uncertainty on Dynamic Asset Allocation," Journal of Finance, American Finance Association, vol. 56(1), pages 205-246, February.
    7. 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..
    8. Frank Riedel, 2000. "Decreasing Yield Curves in a Model with an Unknown Constant Growth Rate," Review of Finance, European Finance Association, vol. 4(1), pages 51-67.
    9. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    10. M. J. Brennan, 1998. "The Role of Learning in Dynamic Portfolio Decisions," Review of Finance, European Finance Association, vol. 1(3), pages 295-306.
    11. Courtadon, Georges, 1982. "The Pricing of Options on Default-Free Bonds," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 17(1), pages 75-100, March.
    12. Andrew Carverhill, 1994. "When Is The Short Rate Markovian?," Mathematical Finance, Wiley Blackwell, vol. 4(4), pages 305-312, October.
    13. Dothan, L. Uri, 1978. "On the term structure of interest rates," Journal of Financial Economics, Elsevier, vol. 6(1), pages 59-69, March.
    14. David Feldman, 2003. "The Term Structure of Interest Rates: Bounded or Falling?," Review of Finance, European Finance Association, vol. 7(1), pages 103-113.
    15. Ho, Thomas S Y & Lee, Sang-bin, 1986. "Term Structure Movements and Pricing Interest Rate Contingent Claims," Journal of Finance, American Finance Association, vol. 41(5), pages 1011-1029, December.
    16. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-887, September.
    17. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    18. David Feldman, 1989. "The Term Structure of Interest Rates in a Partially Observable Economy," Journal of Finance, American Finance Association, vol. 44(3), pages 789-812, July.
    19. 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.
    20. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-1445, November.
    21. Brennan, Michael J. & Schwartz, Eduardo S., 1979. "A continuous time approach to the pricing of bonds," Journal of Banking & Finance, Elsevier, vol. 3(2), pages 133-155, July.
    22. David Feldman, 2001. "Production and the Real Rate of Interest: A Sample Path Equilibrium," Review of Finance, European Finance Association, vol. 5(3), pages 239-267.
    23. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    24. Detemple, Jerome B., 1991. "Further results on asset pricing with incomplete information," Journal of Economic Dynamics and Control, Elsevier, vol. 15(3), pages 425-453, July.
    25. Detemple, Jerome B., 2002. "Asset pricing in an intertemporal partially-revealing rational expectations equilibrium," Journal of Mathematical Economics, Elsevier, vol. 38(1-2), pages 219-248, September.
    26. Michael J. Brennan and Eduardo S. Schwartz., 1979. "A Continuous-Time Approach to the Pricing of Bonds," Research Program in Finance Working Papers 85, University of California at Berkeley.
    27. Detemple, Jerome B, 1986. "Asset Pricing in a Production Economy with Incomplete Information," Journal of Finance, American Finance Association, vol. 41(2), pages 383-391, June.
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    Cited by:

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    2. Anh Ngoc Lai & Constantin Mellios, 2016. "Valuation of commodity derivatives with an unobservable convenience yield," Post-Print halshs-01183166, HAL.

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