  Although financial models violate ergodicity in general, observing the
ergodic behavior in the markets is not rare. Policymakers and market
participants control the market behavior in critical and emergency states,
which leads to some degree of ergodicity as their actions are intentional. In
this paper, we define a parametric operator that acts on the space of positive
stochastic processes, transforming a class of positive stochastic processes
into mean-ergodic processes. With this mechanism, we extract the data regarding
the ergodic behavior hidden in the financial model, apply it to mathematical
finance, and establish a novel method for pricing contingent claims. We provide
some empirical examples and compare the results with existing ones to
demonstrate the efficacy of this new approach.
