Defaultable perpetual Russian option Under a last passage time model

TL;DR

This paper derives a valuation formula for a defaultable perpetual Russian option in a Black-Scholes market, where default is modeled as the last passage time of the stock's maximum.

Contribution

It introduces a novel model where default occurs at the last passage time of the stock's maximum, extending valuation methods for path-dependent default events.

Findings

Provides a closed-form valuation formula for the option.

Models default as a non-stopping time based on the stock's maximum.

Extends classical models to incorporate path-dependent default risk.

Abstract

In this article we provide a valuation formula for a defaultable perpetual Russian option in the Black-Scholes market where the default time is modelled as the last passage time of the running maximum of the stock price. In this setting, default occurs when the stock price fails to exceed its historical maximum, leading to a non-stopping time that depends on the path of the underlying asset.