Phase transition in a log-normal Markov functional model

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Abstract

We derive the exact solution of a one-dimensional Markov functional model with log normally distributed interest rates and constant volatility 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, at which certain expectation values display nonanalytical behavior as a function of 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.

Original languageEnglish
Article number013301
JournalJournal of Mathematical Physics
Volume52
Issue number1
DOIs
StatePublished - 5 Jan 2011

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