Pricing Derivatives in Hermite Markets

TL;DR

This paper introduces Hermite fractional markets driven by multidimensional Hermite motions, deriving conditions for no-arbitrage, market completeness, and pricing of derivatives including bonds, forwards, and futures with associated PDEs.

Contribution

It presents a novel framework for pricing derivatives in Hermite markets, encompassing multivariate fractional Brownian and Rosenblatt motions, with new no-arbitrage and completeness conditions.

Findings

Hermite markets include fractional Brownian and Rosenblatt markets

Derived PDEs for derivative pricing in Hermite markets

Established no-arbitrage and market completeness conditions

Abstract

We introduce Hermite fractional financial markets, where market uncertainties are described by multidimensional Hermite motions. Hermite markets include as particular cases financial markets driven by multivariate fractional Brownian motion and multivariate Rosenblatt motion. Conditions for no-arbitrage and market completeness for Hermite markets are derived. Perpetual derivatives, bonds forwards, and futures are priced. The corresponding partial and partial-differential equations are derived.