Computation of first-order Greeks for barrier options using chain rules for Wiener path integrals

TL;DR

This paper introduces a novel chain rule approach for Wiener path integrals to efficiently compute first-order Greeks of barrier options with complex, path-dependent payoffs and time-dependent triggers, validated by numerical tests.

Contribution

It develops new chain rules for Wiener path integrals specifically tailored for barrier options with complex, path-dependent features and time-dependent triggers.

Findings

Effective computation of Greeks demonstrated through numerical examples

New chain rules improve accuracy and efficiency for path-dependent barrier options

Method applicable to European, Lookback, and Asian options with time-dependent triggers

Abstract

This paper presents a new methodology to compute first-order Greeks for barrier options under the framework of path-dependent payoff functions with European, Lookback, or Asian type and with time-dependent trigger levels. In particular, we develop chain rules for Wiener path integrals between two curves that arise in the computation of first-order Greeks for barrier options. We also illustrate the effectiveness of our method through numerical examples.