From Black-Scholes and Dupire formulae to last passage times of local martingales. Part B : The finite time horizon

TL;DR

This paper explores the mathematical properties of local martingales, focusing on last passage times within finite time horizons, extending classical financial models like Black-Scholes and Dupire formulae.

Contribution

It advances the understanding of local martingales' last passage times over finite horizons, building on foundational models in mathematical finance.

Findings

Characterization of last passage times for local martingales

Extension of Black-Scholes and Dupire formulae to finite horizons

New theoretical insights into martingale behavior over finite periods

Abstract

These notes are the second half of the contents of the course given by the second author at the Bachelier Seminar (8-15-22 February 2008) at IHP. They also correspond to topics studied by the first author for her Ph.D.thesis.