Pricing complexity options

TL;DR

This paper investigates options that pay based on the complexity deficiency of stock price sequences, analyzing their prices both numerically and theoretically for different complexity measures.

Contribution

It introduces the concept of complexity-based options and provides numerical and theoretical pricing methods for automatic and Kolmogorov complexities.

Findings

Numerical pricing of options based on automatic complexity.

Theoretical analysis of options using Kolmogorov complexity.

Comparison of run complexity with automatic complexity.

Abstract

We consider options that pay the complexity deficiency of a sequence of up and down ticks of a stock upon exercise. We study the price of European and American versions of this option numerically for automatic complexity, and theoretically for Kolmogorov complexity. We also consider run complexity, which is a restricted form of automatic complexity.