Non-extensive minimal entropy martingale measures and semi-Markov regime switching interest rate modeling

Abstract

A minimal entropy martingale measure problem is studied to investigate risk-neutral densities and interest rate modelling. Hunt & Devolder focused on the method of Shannon minimal entropy martingale measure to select the best measure among all the equivalent martingale measures and, proposed a generalization of the Ho & Lee model in the semi-Markov regime-switching framework [ 1 ]. We formulate and solve the optimization problem of Hunt & Devolder for deriving risk-neutral densities using a new non-extensive entropy measure [ 2 ]. We use the Lambert function and a new type of approach to obtain results without depending on stochastic calculus techniques.