Preliminary remarks on option pricing and dynamic hedging

TL;DR

This paper introduces a new perspective on option pricing and dynamic hedging by leveraging an arbitrage principle and trend analysis, simplifying complex issues like jumps in underlying assets through trend integration.

Contribution

It presents a novel approach that incorporates trends into option pricing and hedging, based on a theorem from 1995, offering clearer insights into complex market behaviors.

Findings

Incorporating trends simplifies understanding of jumps in asset prices.

Computer experiments validate the proposed trend-based approach.

The method provides a straightforward framework for complex market phenomena.

Abstract

An elementary arbitrage principle and the existence of trends in financial time series, which is based on a theorem published in 1995 by P. Cartier and Y. Perrin, lead to a new understanding of option pricing and dynamic hedging. Intricate problems related to violent behaviors of the underlying, like the existence of jumps, become then quite straightforward by incorporating them into the trends. Several convincing computer experiments are reported.