Work

Applications of the Fractional Diffusion Equation to Option Pricing and Risk Calculations

Year: 2019

Type: article

Abstract: In this article, we first provide a survey of the exponential option pricing models and show that in the framework of the risk-neutral approach, they are governed by the space-fractional diffusion equation. Then, we introduce a more general class of models based on the space-time-fractional diffusion equation and recall some recent results in this field concerning the European option pricing and the risk-neutral parameter. We proceed with an extension of these results to the class of exotic options. In particular, we show that the call and put prices can be expressed in the form of simple power series in terms of the log-forward moneyness and the risk-neutral parameter. Finally, we provide the closed-form formulas for the first and second order risk sensitivities and study the dependencies of the portfolio hedging and profit-and-loss calculations upon the model parameters.

Source: Mathematics

DOI: 10.3390/math7090796

Authors: Jean-Philippe Aguilar, Jan Korbel, Yuri Luchko

Institutions: Banque Populaire, Complexity Science Hub, Czech Technical University in Prague, Medical University of Vienna, Berliner Hochschule für Technik

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: gold

Estimated APC paid: $1,216

Funders: Grantová Agentura České Republiky, Austrian Science Fund