Phase transition in a log-normal Markov functional model
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.
Keywords
Cite
@article{arxiv.1007.0691,
title = {Phase transition in a log-normal Markov functional model},
author = {Dan Pirjol},
journal= {arXiv preprint arXiv:1007.0691},
year = {2015}
}
Comments
9 pages, 5 figures. v2: Added asymptotic expressions for the convexity-adjusted Libors in the small and large volatility limits. v3: Added one reference. Final version to appear in Journal of Mathematical Physics