A One-Factor Conditionally Linear Commodity Pricing Model under Partial Information

TL;DR

This paper develops a one-factor commodity pricing model with hidden parameters under partial information, providing explicit pricing formulas and a novel filtering method for unobservable variables.

Contribution

It introduces a conditionally linear filtering approach to compute pricing and hedging formulas in a partially observable stochastic environment.

Findings

Explicit no-arbitrage pricing formulas derived

Utility indifference pricing for illiquid assets established

A new Bayesian filtering method for hidden parameters proposed

Abstract

A one-factor asset pricing model with an Ornstein--Uhlenbeck process as its state variable is studied under partial information: the mean-reverting level and the mean-reverting speed parameters are modeled as hidden/unobservable stochastic variables. No-arbitrage pricing formulas for derivative securities written on a liquid asset and exponential utility indifference pricing formulas for derivative securities written on an illiquid asset are presented. Moreover, a conditionally linear filtering result is introduced to compute the pricing/hedging formulas and the Bayesian estimators of the hidden variables.