The financial value of knowing the distribution of stock prices in discrete market models

TL;DR

This paper derives an explicit formula for the value of weak information in discrete market models, applicable to various utility functions, and provides calculations for binomial and trinomial models.

Contribution

It introduces a general explicit formula for the value of weak information in discrete-time, complete market models with finite outcomes, including binomial and trinomial cases.

Findings

Explicit formula for weak information value derived

Calculations demonstrated for binomial models

Discussion extended to trinomial models

Abstract

An explicit formula is derived for the value of weak information in a discrete time model that works for a wide range of utility functions including the logarithmic and power utility. We assume a complete market with a finite number of assets and a finite number of possible outcomes. Explicit calculations are performed for a binomial model with two assets. The case of trinomial models is also discussed.