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Pricing Interest Rate Exotics in Multi-Factor Gaussian Interest Rate Models

Author

Listed:
  • Les Clewlow

    (Lacima Group)

  • Chris Strickland

    (Lacima Group)

Abstract

For many interest rate exotic options, for example options on the slope of the yield curve or American featured options, a one factor assumption for term structure evolution is inappropriate. These options derive their value from changes in the slope or cuvature of the yield curve and hence are more realistically priced with multiple factor models. However, efficient construction of short rate trees becomes computationally intractable as we increase the number of factors and in particular as we move to non-Markovian models. In this paper we describe a general framework for pricing a wide range of interest rate exotic options under a very general family of multi-factor Gaussian interest rate models. Our framework is based on a computationally efficient implementation of Monte Carlo integration utilising analytical approximations as control variates. These techniques extend the analysis of Clewlow, Pang and Strickland [1997] for pricing interest rate caps and swaptions.

Suggested Citation

  • Les Clewlow & Chris Strickland, 1998. "Pricing Interest Rate Exotics in Multi-Factor Gaussian Interest Rate Models," Research Paper Series 2, Quantitative Finance Research Centre, University of Technology, Sydney.
    • Handle: RePEc:uts:rpaper:2
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    File URL: http://www.qfrc.uts.edu.au/research/research_papers/rp2.pdf
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    References listed on IDEAS

    as
    1. 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..
    2. 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.
    3. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    4. Amin, Kaushik I. & Morton, Andrew J., 1994. "Implied volatility functions in arbitrage-free term structure models," Journal of Financial Economics, Elsevier, vol. 35(2), pages 141-180, April.
    5. Robert A. Jarrow & Arkadev Chatterjea, 2019. "The Heath–Jarrow–Morton Libor Model," World Scientific Book Chapters, in: An Introduction to Derivative Securities, Financial Markets, and Risk Management, chapter 25, pages 618-654, World Scientific Publishing Co. Pte. Ltd..
    6. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
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    Cited by:

    1. João Pedro Vidal Nunes, 2004. "MultiFactor Valuation of Floating Range Notes," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 79-97, January.
    2. Marat Kramin & Saikat Nandi & Alexander Shulman, 2008. "A multi-factor Markovian HJM model for pricing American interest rate derivatives," Review of Quantitative Finance and Accounting, Springer, vol. 31(4), pages 359-378, November.
    3. Marat Kramin & Timur Kramin & Stephen Young & Venkat Dharan, 2005. "A Simple Induction Approach and an Efficient Trinomial Lattice for Multi-State Variable Interest Rate Derivatives Models," Review of Quantitative Finance and Accounting, Springer, vol. 24(2), pages 199-226, January.

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