Analytical Approximation Formula for Barrier Option Prices under the Regime-Switching Model

Abstract

In the article barrier options are analytically evaluated under the regime-switching model, with the volatility of the underlying price being allowed to jump between different states following a Markov chain. The target barrier option prices are expressed in a Fourier cosine series after a particular approximation formula is obtained. The accuracy and efficiency of the newly derived formula are demonstrated through numerical experiments, demonstrating the formula’s potential for practical applications.

TOPICS: Analysis of individual factors/risk premia, factor-based models, options

Key Findings

• • Barrier options are analytically evaluated under the regime-switching model.

• • This approximation formula is written in the form of a converged Fourier cosine series.

• • The formula is shown to be very accurate and efficient, and has a great potential to be applied in practice.