Perpetual American options within CTRW's

TL;DR

This paper models perpetual American options using continuous-time random walks, providing a flexible framework that aligns with classical formulas under standard assumptions but also adapts to complex market conditions.

Contribution

It introduces a CTRW-based model for perpetual American options, extending traditional methods to accommodate more exotic market dynamics.

Findings

Option prices match classical formulas under standard assumptions.

Model is adaptable to complex, non-standard market conditions.

Provides a new framework for option valuation at the tick-to-tick level.

Abstract

Continuous-time random walks are a well suited tool for the description of market behaviour at the smallest scale: the tick-to-tick evolution. We will apply this kind of market model to the valuation of perpetual American options: derivatives with no maturity that can be exercised at any time. Our approach leads to option prices that fulfil financial formulas when canonical assumptions on the dynamics governing the process are made, but it is still suitable for more exotic market conditions.