Conditional-Mean Hedging Under Transaction Costs in Gaussian Models

TL;DR

This paper develops a prediction formula for Gaussian Volterra processes and applies it to conditional-mean hedging in models with transaction costs, extending classical Black-Scholes frameworks.

Contribution

It introduces a prediction law for regular invertible Gaussian Volterra processes and applies it to hedging strategies under transaction costs in generalized models.

Findings

Derived a formula for prediction laws of Gaussian Volterra processes

Extended hedging strategies to models with non-standard Gaussian drivers

Demonstrated applicability to fractional and mixed fractional Brownian motions

Abstract

We consider so-called regular invertible Gaussian Volterra processes and derive a formula for their prediction laws. Examples of such processes include the fractional Brownian motions and the mixed fractional Brownian motions. As an application, we consider conditional-mean hedging under transaction costs in Black-Scholes type pricing models where the Brownian motion is replaced with a more general regular invertible Gaussian Volterra process.