L\'{e}vy driven models and derivative pricing

TL;DR

This paper introduces a novel method for derivative pricing based on Shannon's Information Theory, utilizing $bb$-analyticity of Lévy models to derive new pricing integral representations and algorithms.

Contribution

It presents the concept of $bb$-analyticity for Lévy models and develops a general algorithm for European call option pricing based on this framework.

Findings

Le9vy models are shown to be $bb$-analytic in applications.

New representations of the pricing integral are derived.

A general algorithm for European call options is developed.

Abstract

We develop a general method for derivative pricing. This approach has its roots in Shannon's Information Theory. The notion of $\lambda$-analyticity of L\'{e}vy models is introduced on the basis of which new representations of the pricing integral are obtained. It is shown that popular in applications L\'{e}vy models are $\lambda$-analytic. We apply these results to derive a general algorithm for pricing of European call options.