Strict local martingales and bubbles

TL;DR

This paper investigates asset price bubbles modeled as strict local martingales, exploring associated measures and the impact on option prices, including path-dependent options and last passage times.

Contribution

It introduces a detailed analysis of measures related to strict local martingales and characterizes the default term in option prices caused by bubbles.

Findings

Associated measures for strict local martingales are characterized.

The default term in option prices due to bubbles is explicitly determined.

Results include formulas for path-dependent options and last passage times.

Abstract

This paper deals with asset price bubbles modeled by strict local martingales. With any strict local martingale, one can associate a new measure, which is studied in detail in the first part of the paper. In the second part, we determine the "default term" apparent in risk-neutral option prices if the underlying stock exhibits a bubble modeled by a strict local martingale. Results for certain path dependent options and last passage time formulas are given.