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Stochastic duration and fast coupon bond option pricing in multi-factor models

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  • Claus Munk

Abstract

Generalizing Cox, Ingersoll, and Ross (1979), this paper defines the stochastic duration of a bond in a general multi-factor diffusion model as the time to maturity of the zero-coupon bond with the same relative volatility as the bond. Important general properties of the stochastic duration measure are derived analytically, and the stochastic duration is studied in detail in various well-known models. It is also demonstrated by analytical arguments and numerical examples that the price of a European option on a coupon bond (and, hence, of a European swaption) can be approximated very accurately by a multiple of the price of a European option on a zero-coupon bond with a time to maturity equal to the stochastic duration of the coupon bond. Copyright Kluwer Academic Publishers 1999

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  • Claus Munk, 1999. "Stochastic duration and fast coupon bond option pricing in multi-factor models," Review of Derivatives Research, Springer, vol. 3(2), pages 157-181, May.
    • Handle: RePEc:kap:revdev:v:3:y:1999:i:2:p:157-181
    DOI: 10.1023/A:1009654427422
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    2. Vincenzo Russo & Gabriele Torri, 2019. "Calibration of one-factor and two-factor Hull–White models using swaptions," Computational Management Science, Springer, vol. 16(1), pages 275-295, February.
    3. João Pedro Vidal Nunes & Pedro Miguel Silva Prazeres, 2014. "Pricing Swaptions Under Multifactor Gaussian Hjm Models," Mathematical Finance, Wiley Blackwell, vol. 24(4), pages 762-789, October.
    4. João Nunes, 2011. "American options and callable bonds under stochastic interest rates and endogenous bankruptcy," Review of Derivatives Research, Springer, vol. 14(3), pages 283-332, October.
    5. David F. Schrager & Antoon A. J. Pelsser, 2006. "Pricing Swaptions And Coupon Bond Options In Affine Term Structure Models," Mathematical Finance, Wiley Blackwell, vol. 16(4), pages 673-694, October.
    6. Hitesh Doshi & Hyung Joo Kim & Sang Byung Seo, 2023. "Options on Interbank Rates and Implied Disaster Risk," Finance and Economics Discussion Series 2023-054, Board of Governors of the Federal Reserve System (U.S.).
    7. Anders B. Trolle & Eduardo S. Schwartz, 2006. "A General Stochastic Volatility Model for the Pricing and Forecasting of Interest Rate Derivatives," NBER Working Papers 12337, National Bureau of Economic Research, Inc.
    8. Dai, Qiang & Singleton, Kenneth J., 2003. "Fixed-income pricing," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 20, pages 1207-1246, Elsevier.
    9. Frédéric Godin & Ramin Eghbalzadeh & Patrice Gaillardetz, 2023. "Pricing swaptions and zero-coupon futures options under the discrete-time arbitrage-free Nelson–Siegel model," Review of Derivatives Research, Springer, vol. 26(2), pages 171-206, October.
    10. Joel R. Barber, 2005. "Bond Option Valuation for Non‐Markovian Interest Rate Processes," The Financial Review, Eastern Finance Association, vol. 40(4), pages 519-532, November.
    11. Patrick Büchel & Michael Kratochwil & Maximilian Nagl & Daniel Rösch, 2022. "Deep calibration of financial models: turning theory into practice," Review of Derivatives Research, Springer, vol. 25(2), pages 109-136, July.
    12. Luís Oliveira & João Vidal Nunes & Luís Malcato, 2014. "The performance of deterministic and stochastic interest rate risk measures:," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 13(3), pages 141-165, December.
    13. Anders B. Trolle & Eduardo S. Schwartz, 2009. "A General Stochastic Volatility Model for the Pricing of Interest Rate Derivatives," The Review of Financial Studies, Society for Financial Studies, vol. 22(5), pages 2007-2057, May.
    14. Oh Kwon, 2007. "Duration, factor sensitivities, and interest rate Greeks," Annals of Finance, Springer, vol. 3(4), pages 471-486, October.
    15. Bueno-Guerrero, Alberto & Moreno, Manuel & Navas, Javier F., 2020. "Valuation of caps and swaptions under a stochastic string model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 559(C).
    16. James M. O'Brien, 2000. "Estimating the value and interest rate risk of interest-bearing transactions deposits," Finance and Economics Discussion Series 2000-53, Board of Governors of the Federal Reserve System (U.S.).

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