Equity-linked security pricing and Greeks at arbitrary intermediate times using Brownian bridge

Hanbyeol Jang, Jian Wang, Junseok Kim

Research output: Contribution to journalArticle

Abstract

We develop a numerical algorithm for predicting prices and Greeks of equity-linked securities (ELS) with a knock-in barrier at any time over the total time period from issue date to maturity by using Monte Carlo simulation (MCS). The ELS is one of the most important financial derivatives in Korea. In the proposed algorithm, first we calculate the probability (0 ≤ p ≤ 1 {0\leq p\leq 1}) that underlying asset price never hits the knock-in barrier up to the intermediate evaluation date. Second, we compute two option prices V n k {V{nk}} and V k {V{k}}, where Vnk {V{nk}} is the option value which knock-in event does not occur and V k {V{k}} is the option value which knock-in event occurs. Finally, we predict the option value with a weighted average. We apply the proposed algorithm to two- and three-asset ELS. We provide the pseudo-numerical algorithm and computational results to demonstrate the usefulness of the proposed method.

Original languageEnglish
JournalMonte Carlo Methods and Applications
DOIs
Publication statusPublished - 2019 Jan 1

Keywords

  • Brownian bridge
  • Equity-linked securities
  • Monte Carlo simulation
  • option pricing

ASJC Scopus subject areas

  • Statistics and Probability
  • Applied Mathematics

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