Classification of barrier options

TL;DR

This paper investigates the precise conditions under which barrier options simplify into standard options as pricing parameters vary, using a probability-based method to identify critical initial stock prices within a specified accuracy.

Contribution

It introduces a novel probability-based approach to determine critical stock prices where barrier options degenerate, enhancing understanding of option behavior under parameter changes.

Findings

Identifies critical stock prices for barrier option degeneration.

Provides a method to determine when barrier options simplify.

Enhances option pricing accuracy understanding.

Abstract

For a given level of accuracy in option prices, the paper considers the problem of deciding when exactly, as one or more of the pricing parameters change, a barrier option degenerates into a simpler type of option. This problem is meaningful in the real world where option prices are always determined within a certain level of accuracy. The problem is reduced to finding certain critical values of the initial stock price, and this is achieved through a probability-based approach.