Call option prices based on Bessel processes

TL;DR

This paper investigates call option prices derived from Bessel strict local martingales, demonstrating their integrability over time and exploring the resulting probability densities, thus extending recent theoretical work on local martingales and financial bubbles.

Contribution

It provides new insights into the integrability and density functions of call options linked to Bessel strict local martingales, expanding the understanding of such models in financial mathematics.

Findings

Call option prices are integrable over time.

Probability densities associated with these options are characterized.

Extends theoretical framework for local martingale-based models.

Abstract

As a complement to some recent work by Pal and Protter, "Strict local martingales, bubbles, and no early exercise", we show that the call option prices associated with the Bessel strict local martingales are integrable over time, and we discuss the probability densities obtained thus.