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Fair prices under a unified lattice approach for interest rate derivatives

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  • Giacomo Morelli

    (LUISS University)

Abstract

An open question in interest rates derivative pricing is whether the price of the contracts should be computed by means of a multi-curve approach (different yield curves for discounting and forwarding) or by using a single curve (just one yield curve both for discounting and forwarding). The answer is of primary importance for financial markets as it allows to define a class of fair contracts. This paper calculates and compares the price of a simple swap within both multi-curve and single curve approaches and proposes a generalization of the lattice approach, which is usually used to approximate short interest rate models in the multi-curve framework. As an example, I show how to use the Black et al. (Financ Anal J 46(1):33–39, 1990) interest rate model on binomial lattice in multi-curve framework and calculate the price of the 2–8 period swaption with a single (LIBOR) curve and two-curve (OIS+LIBOR) approaches. Such technique can be used for pricing any interest rate based contract.

Suggested Citation

  • Giacomo Morelli, 2021. "Fair prices under a unified lattice approach for interest rate derivatives," Annals of Operations Research, Springer, vol. 299(1), pages 429-441, April.
    • Handle: RePEc:spr:annopr:v:299:y:2021:i:1:d:10.1007_s10479-019-03209-y
    DOI: 10.1007/s10479-019-03209-y
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    References listed on IDEAS

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    1. Michael Johannes & Suresh Sundaresan, 2007. "The Impact of Collateralization on Swap Rates," Journal of Finance, American Finance Association, vol. 62(1), pages 383-410, February.
    2. 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(4), pages 419-440, December.
    3. Uri Ron, 2000. "A Practical Guide to Swap Curve Construction," Staff Working Papers 00-17, Bank of Canada.
    4. Masaaki Fujii & Yasufumi Shimada & Akihiko Takahashi, 2009. "A Market Model of Interest Rates with Dynamic Basis Spreads in the presence of Collateral and Multiple Currencies," CARF F-Series CARF-F-196, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Apr 2011.
    5. Henrard, Marc, 2007. "The irony in the derivatives discounting," MPRA Paper 3115, University Library of Munich, Germany.
    6. Masaaki Kijima & Keiichi Tanaka & Tony Wong, 2009. "A multi-quality model of interest rates," Quantitative Finance, Taylor & Francis Journals, vol. 9(2), pages 133-145.
    7. Clifford A. Ball & Walter N. Torous, 1999. "The Stochastic Volatility of Short‐Term Interest Rates: Some International Evidence," Journal of Finance, American Finance Association, vol. 54(6), pages 2339-2359, December.
    8. Masaaki Fujii & Yasufumi Shimada & Akihiko Takahashi, 2009. "A Note on Construction of Multiple Swap Curves with and without Collateral," CARF F-Series CARF-F-154, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Jan 2010.
    9. 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.
    10. Tse, Y. K., 1995. "Some international evidence on the stochastic behavior of interest rates," Journal of International Money and Finance, Elsevier, vol. 14(5), pages 721-738, October.
    11. 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.
    12. Rama Cont & Andreea Minca, 2016. "Credit default swaps and systemic risk," Annals of Operations Research, Springer, vol. 247(2), pages 523-547, December.
    13. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    14. Nikolaos Karouzakis & John Hatgioannides & Kostas Andriosopoulos, 2018. "Convexity adjustment for constant maturity swaps in a multi-curve framework," Annals of Operations Research, Springer, vol. 266(1), pages 159-181, July.
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    Cited by:

    1. Taiga Saito & Shivam Gupta, 2022. "Big Data Applications with Theoretical Models and Social Media in Financial Management," CIRJE F-Series CIRJE-F-1205, CIRJE, Faculty of Economics, University of Tokyo.
    2. Taiga Saito & Shivam Gupta, 2022. "Big data applications with theoretical models and social media in financial management," CARF F-Series CARF-F-550, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.

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    More about this item

    Keywords

    Interest rates; Single curve; Multiple curve; Derivative pricing; Fair contracts;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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