Generalized Filtrations and Its Application to Binomial Asset Pricing Models

TL;DR

This paper introduces a generalized filtration framework that models information loss over time and applies it to develop a binomial asset pricing model, enabling valuation of financial claims under non-standard information structures.

Contribution

It presents a novel generalized filtration concept and demonstrates its application to binomial asset pricing, extending traditional models to account for information forgetting.

Findings

Model captures agents forgetting information at specific times

Valuations of financial claims are derived under the new filtration

Framework broadens the scope of asset pricing models

Abstract

We introduce generalized filtration with which we can represent situations such as some agents forget information at some specific time. The filtration is defined as a functor to a category Prob whose objects are all probability spaces and whose arrows correspond to measurable functions satisfying an absolutely continuous requirement [Adachi and Ryu, 2019]. As an application of a generalized filtration, we develop a binomial asset pricing model, and investigate the valuations of financial claims along this type of non-standard filtrations.