PT  - JOURNAL ARTICLE
AU  - Holger Fink
TI  - An Arbitrage-Free Real-World Model for Fractional Option Prices
AID  - 10.3905/jod.2021.1.128
DP  - 2021 Mar 25
TA  - The Journal of Derivatives
PG  - jod.2021.1.128
4099  - https://pm-research.com/content/early/2021/03/25/jod.2021.1.128.short
4100  - https://pm-research.com/content/early/2021/03/25/jod.2021.1.128.full
AB  - I introduce a new model class driven by a certain transformation of fractional Lévy processes with an additional jump part. Not only am I able to show that these models are free of arbitrage and allow for an explicit measure change to an equivalent martingale measure, but they also contain the Black-Scholes setting as a special case. Therefore, this fractional model class can be viewed as a natural no-arbitrage extension of the classical setup.TOPICS: Statistical methods, derivatives, optionsKey Findings▪ I present a model class driven by (a transformation of) fractional Lévy processes, which still fits into the classical semimartingale framework.▪ Derivative prices are discounted conditional expectations with respect to the driving fractional Lévy processes.▪ The classical Black-Scholes and Merton models are nested within the presented framework.