Persistence of Averages in Financial Markov Switching Models: A Large Deviations Approach

Abstract

The behavior of time averages, or functions of them, is important in quantitative research. Over an investment horizon, both the time-averaged number of loan defaults and the time-averaged log gross returns from securities investment, a.k.a. the continuously compounded cumulative rate of return (CROR), are important random variables affecting the performance of loan and securities portfolios, respectively. In ergodic models, the randomness in such averages is eliminated only asymptotically. The statistical theory of Large Deviations provides simply computed and useful tools for analyzing this persistence, and is developed and applied to Markov Switching models of loan defaults and securities portfolio choice.

Keywords: Econophysics, Large Deviations, Markov Switching Models

JEL Classification: B26, C58, G11