### 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 V_{nk} {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 language | English |
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Journal | Monte Carlo Methods and Applications |

DOIs | |

Publication status | Published - 2019 Jan 1 |

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### Keywords

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

### ASJC Scopus subject areas

- Statistics and Probability
- Applied Mathematics

### Cite this

**Equity-linked security pricing and Greeks at arbitrary intermediate times using Brownian bridge.** / Jang, Hanbyeol; Wang, Jian; Kim, Junseok.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Equity-linked security pricing and Greeks at arbitrary intermediate times using Brownian bridge

AU - Jang, Hanbyeol

AU - Wang, Jian

AU - Kim, Junseok

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - Brownian bridge

KW - Equity-linked securities

KW - Monte Carlo simulation

KW - option pricing

UR - http://www.scopus.com/inward/record.url?scp=85073384548&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85073384548&partnerID=8YFLogxK

U2 - 10.1515/mcma-2019-2048

DO - 10.1515/mcma-2019-2048

M3 - Article

AN - SCOPUS:85073384548

JO - Monte Carlo Methods and Applications

JF - Monte Carlo Methods and Applications

SN - 0929-9629

ER -