Variance Optimal Hedging for continuous time processes with independent increments and applications

TL;DR

This paper develops explicit hedging strategies for vanilla options when the underlying asset follows a process with independent increments, enabling efficient solutions for mean variance hedging, with applications to electricity markets.

Contribution

It provides an explicit Föllmer-Schweizer decomposition for processes with independent increments, facilitating practical hedging algorithms for complex financial models.

Findings

Explicit formulas for hedging in PII models

Efficient algorithm for mean variance hedging

Successful application to electricity market models

Abstract

For a large class of vanilla contingent claims, we establish an explicit F\"ollmer-Schweizer decomposition when the underlying is a process with independent increments (PII) and an exponential of a PII process. This allows to provide an efficient algorithm for solving the mean variance hedging problem. Applications to models derived from the electricity market are performed.