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Markov Market Model Consistent With Cap Smile

Author

Listed:
  • P. BALLAND

    (Merrill Lynch International, 25 Ropemaker Street, London EC2Y 9LY, UK)

  • L. P. HUGHSTON

    (Department of Mathematics, King's College London, The Strand, London WC2R 2LS, UK)

Abstract

New interest rate models have emerged recently in which distributional assumptions are made directly on financial observables. In these "Market Models" the Libor rates have a log-normal distribution in the corresponding forward measure, and caps are priced according to the Black–Scholes formula. These models present two disadvantages. First, Libor rates do not in reality have a log-normal distribution since the implied volatility of a cap depends typically on the strike. Second, these models are difficult to use for pricing derivatives other than caps. In this paper, we extend these models to allow for a broader class of Libor rate distributions. In particular, we construct multi-factor Market Models that are consistent with an initial cap smile surface, and have the useful feature of exhibiting Markovian Libor rates. We show that these Markov Market Models can be used relatively easily to price complex Libor derivatives, such as Bermudan swaptions, captions or flexi-caps, by construction of a tree of Libor rates.

Suggested Citation

  • P. Balland & L. P. Hughston, 2000. "Markov Market Model Consistent With Cap Smile," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(02), pages 161-181.
    • Handle: RePEc:wsi:ijtafx:v:03:y:2000:i:02:n:s0219024900000085
    DOI: 10.1142/S0219024900000085
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    Citations

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    Cited by:

    1. Dan Pirjol, 2013. "Explosive Behavior In A Log-Normal Interest Rate Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(04), pages 1-23.
    2. Dan Pirjol, 2016. "Eurodollar futures pricing in log-normal interest rate models in discrete time," Applied Mathematical Finance, Taylor & Francis Journals, vol. 23(6), pages 445-464, November.
    3. Joanne Kennedy & Phil Hunt & Antoon Pelsser, 2000. "Markov-functional interest rate models," Finance and Stochastics, Springer, vol. 4(4), pages 391-408.
    4. Junwu Gan, 2014. "An almost Markovian LIBOR market model calibrated to caps and swaptions," Quantitative Finance, Taylor & Francis Journals, vol. 14(11), pages 1937-1959, November.
    5. Dan Pirjol, 2010. "Phase transition in a log-normal Markov functional model," Papers 1007.0691, arXiv.org, revised Jan 2011.

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