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Phase transition in a log-normal Markov functional model

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  • Dan Pirjol

Abstract

We derive the exact solution of a one-dimensional Markov functional model with log-normally distributed interest rates in discrete time. The model is shown to have two distinct limiting states, corresponding to small and asymptotically large volatilities, respectively. These volatility regimes are separated by a phase transition at some critical value of the volatility. We investigate the conditions under which this phase transition occurs, and show that it is related to the position of the zeros of an appropriately defined generating function in the complex plane, in analogy with the Lee-Yang theory of the phase transitions in condensed matter physics.

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  • Dan Pirjol, 2010. "Phase transition in a log-normal Markov functional model," Papers 1007.0691, arXiv.org, revised Jan 2011.
    • Handle: RePEc:arx:papers:1007.0691
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    References listed on IDEAS

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    1. 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.
    2. Joanne Kennedy & Phil Hunt & Antoon Pelsser, 2000. "Markov-functional interest rate models," Finance and Stochastics, Springer, vol. 4(4), pages 391-408.
    3. 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.
    4. Dothan, L. Uri, 1978. "On the term structure of interest rates," Journal of Financial Economics, Elsevier, vol. 6(1), pages 59-69, March.
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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, 2015. "Hogan-Weintraub singularity and explosive behaviour in the Black-Derman-Toy model," Quantitative Finance, Taylor & Francis Journals, vol. 15(7), pages 1243-1257, July.

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