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A Multifactor Spot Rate Model for the Pricing of Interest Rate Derivatives

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  • Peterson, Sandra
  • Stapleton, Richard C.
  • Subrahmanyam, Marti G.

Abstract

We propose a multifactor model in which the spot rate, LIBOR, follows a lognormal process, with a stochastic conditional mean, under the risk-neutral measure. In addition to the spot rate factor, the second factor is related to the premium of the first futures rate over the spot LIBOR. Similarly, the third factor is related to the premium of the second futures rate over the first futures rate. We calibrate the model to the initial term structure of futures rates and to the implied volatilities of interest rate caplets. We then apply the model to price interest rate derivatives such as European and Bermudan-style swaptions, and yieldspread options. The model can be employed to price more complex interest rate derivatives such as path-dependent derivatives or multi-currency-dependent derivatives because of its Markovian property.

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  • Peterson, Sandra & Stapleton, Richard C. & Subrahmanyam, Marti G., 2003. "A Multifactor Spot Rate Model for the Pricing of Interest Rate Derivatives," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 38(4), pages 847-880, December.
    • Handle: RePEc:cup:jfinqa:v:38:y:2003:i:04:p:847-880_00
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    1. Narasimhan Jegadeesh & George Pennacchi, 1996. "The behavior of interest rates implied by the term structure of Eurodollar future," Proceedings, Federal Reserve Bank of Cleveland, issue Aug, pages 426-451.
    2. Li, Anlong & Ritchken, Peter & Sankarasubramanian, L, 1995. "Lattice Models for Pricing American Interest Rate Claims," Journal of Finance, American Finance Association, vol. 50(2), pages 719-737, June.
    3. Rong Fan & Anurag Gupta & Peter Ritchken, 2003. "Hedging in the Possible Presence of Unspanned Stochastic Volatility: Evidence from Swaption Markets," Journal of Finance, American Finance Association, vol. 58(5), pages 2219-2248, October.
    4. Brennan, Michael J. & Schwartz, Eduardo S., 1982. "An Equilibrium Model of Bond Pricing and a Test of Market Efficiency," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 17(3), pages 301-329, September.
    5. Driessen, Joost & Klaassen, Pieter & Melenberg, Bertrand, 2003. "The Performance of Multi-Factor Term Structure Models for Pricing and Hedging Caps and Swaptions," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 38(3), pages 635-672, September.
    6. repec:bla:jfinan:v:44:y:1989:i:1:p:205-09 is not listed on IDEAS
    7. 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: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    8. Pierluigi Balduzzi & Sanjiv Ranjan Das & Silverio Foresi, 1998. "The Central Tendency: A Second Factor In Bond Yields," The Review of Economics and Statistics, MIT Press, vol. 80(1), pages 62-72, February.
    9. Gupta, Anurag & Subrahmanyam, Marti G., 2000. "An empirical examination of the convexity bias in the pricing of interest rate swaps," Journal of Financial Economics, Elsevier, vol. 55(2), pages 239-279, February.
    10. Dong-Hyun Ahn & Robert F. Dittmar, 2002. "Quadratic Term Structure Models: Theory and Evidence," The Review of Financial Studies, Society for Financial Studies, vol. 15(1), pages 243-288, March.
    11. 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..
    12. Miltersen, Kristian R & Sandmann, Klaus & Sondermann, Dieter, 1997. "Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates," Journal of Finance, American Finance Association, vol. 52(1), pages 409-430, March.
    13. 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.
    14. 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.
    15. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    16. 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.
    17. Peter Ritchken & L. Sankarasubramanian, 1995. "Volatility Structures Of Forward Rates And The Dynamics Of The Term Structure1," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 55-72, January.
    18. Nelson, Daniel B & Ramaswamy, Krishna, 1990. "Simple Binomial Processes as Diffusion Approximations in Financial Models," The Review of Financial Studies, Society for Financial Studies, vol. 3(3), pages 393-430.
    19. Sundaresan, Suresh, 1991. "Futures Prices on Yields, Forward Prices, and Implied Forward Prices from Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 26(3), pages 409-424, September.
    20. 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.
    21. Gregory R. Duffee, 2002. "Term Premia and Interest Rate Forecasts in Affine Models," Journal of Finance, American Finance Association, vol. 57(1), pages 405-443, February.
    22. Broadie, Mark & Glasserman, Paul, 1997. "Pricing American-style securities using simulation," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1323-1352, June.
    23. 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.
    24. Amin, Kaushik I., 1991. "On the Computation of Continuous Time Option Prices Using Discrete Approximations," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 26(4), pages 477-495, December.
    25. Ho, Teng-Suan & Stapleton, Richard C & Subrahmanyam, Marti G, 1995. "Multivariate Binomial Approximations for Asset Prices with Nonstationary Variance and Covariance Characteristics," The Review of Financial Studies, Society for Financial Studies, vol. 8(4), pages 1125-1152.
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    2. Realdon, Marco, 2009. ""Extended Black" term structure models," International Review of Financial Analysis, Elsevier, vol. 18(5), pages 232-238, December.
    3. Deuskar, Prachi & Gupta, Anurag & Subrahmanyam, Marti G., 2008. "The economic determinants of interest rate option smiles," Journal of Banking & Finance, Elsevier, vol. 32(5), pages 714-728, May.

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