• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.24 no.1
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• pp.79-84
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• 2020

In this article, we implement a recently developed fast Monte Carlo simulation (MCS) for pricing equity-linked securities (ELS), which is most commonly issued autocallable structured financial derivative in South Korea, on the mobile platform. The fast MCS is based on Brownian bridge technique. Although mobile platform devices are easy to carry around, mobile platform devices are slow in computation compared to desktop computers. Therefore, it is essential to use a fast algorithm for pricing ELS on the mobile platform. The computational results demonstrate the practicability of Android application implementation for pricing ELS.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.21 no.3
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• pp.181-202
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• 2017

In this paper, we develop a mobile platform for pricing equity linked securities(ELS) using Monte Carlo simulation. Mobile phone or smartphone is an important part of most people's lives and has become an everyday item at the present day. Moreover, importance of technologies for anytime and anywhere is increasing daily. Thus, we construct a mobile computing environment for pricing ELS instead of desktops or laptop computers. We provide a detailed Java programming code and a process manual to easily follow up all processes of this paper.

• The Pure and Applied Mathematics
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• v.28 no.4
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• pp.329-341
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• 2021

In this study, we consider an efficient and accurate finite difference method for the four underlying asset equity-linked securities (ELS). The numerical method is based on the operator splitting method with non-uniform grids for the underlying assets. Even though the numerical scheme is implicit, we solve the system of discrete equations in explicit manner using the Thomas algorithm for the tri-diagonal matrix resulting from the system of discrete equations. Therefore, we can use a relatively large time step and the computation of the ELS option pricing is fast. We perform characteristic computational test. The numerical test confirm the usefulness of the proposed method for pricing the four underlying asset equity-linked securities.

• Communications for Statistical Applications and Methods
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• v.14 no.2
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• pp.413-429
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• 2007

Equity-linked securities (ELS) provide their customers with the return linked to the underlying equity (or equities). Equity-linked products in Korea have recently gained popularity due to relatively low interest rates. This paper discusses an equity-linked security whose principal is not guaranteed. The payoff of the ELS depends on the returns of two underlying assets. This paper presents numerical prices of the proposed product by using Monte-Carlo simulation method. It assumes that the log-returns of two stocks follow either Brownian motion or variance gamma process. Finally, the comparison of the two approaches is discussed.

• Honam Mathematical Journal
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• v.37 no.4
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• pp.441-455
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• 2015

In this paper, we perform a comparison study of explicit and implicit numerical methods for the equity-linked securities (ELS). The option prices of the two-asset ELS are typically computed using an implicit finite diffrence method because an explicit finite diffrence scheme has a restriction for time steps. Nowadays, the three-asset ELS is getting popularity in the real world financial market. In practical applications of the finite diffrence methods in computational finance, we typically use relatively large space steps and small time steps. Therefore, we can use an accurate and effient explicit finite diffrence method because the implementation is simple and the computation is fast. The computational results demonstrate that if we use a large space step, then the explicit scheme is better than the implicit one. On the other hand, if the space step size is small, then the implicit scheme is more effient than the explicit one.

• Communications for Statistical Applications and Methods
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• v.27 no.1
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• pp.79-95
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• 2020

The globalization of financial markets has broadened investment opportunities. International investors' investment portfolios consist of financial instruments from various countries; consequently, the risks associated with economic dependence among countries should be carefully considered. Step-down equity-linked securities (ELS) are a structured financial product that have recently become popular among Korean investors. Payoffs are based on two or three stock indices from different regions; therefore, dependence between the indices should be reflected in the risk analysis. In this study, we consider a regime-switching copula model to describe the joint behavior of two stock indices- the Eurostoxx50 and the Hang Seng China Enterprises Index (HSCEI). These indices are commonly used as underlying assets of step-down ELS. Using historical data, we analyze the risk associated with step-down ELS through the probabilities of early redemption. A regime-switching copula model can accommodate complicated dependence. Thus, it should be considered in the risk analysis of step-down ELS.

• The Korean Journal of Applied Statistics
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• v.24 no.6
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• pp.1021-1031
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• 2011

Equity linked securities are indirect investments where the return of investment depends on the performance of the underlying equities. In this paper, we review the profit structure of typical equity linked securities through a profit diagram and investigate which characteristics of time series at the investment affect the early repayment of the stepdown ELS based on KOSPI 200 and HSI. We also compare VaRs using the empirical distribution function for risk management.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.25 no.3
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• pp.82-92
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• 2021

In this study, we present a fast option pricing method for four asset equity-linked securities (ELS) using Brownian bridge. The proposed method is based on Monte Carlo simulation (MCS) and a Brownian bridge approach. Currently, three asset ELS is the most popular ELS among multi-asset ELSs. However, four asset ELS emerged as an alternative to three asset ELS under low interest rate environment to give higher coupon rate to investors. We describe in detail the computational solution algorithm for the four underlying asset step-down ELS. The numerical tests confirm the accuracy and speed of the method.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.23 no.3
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• pp.237-251
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• 2019

We extend the previous work [J. Korean Soc. Ind. Appl. Math. 21(3) 181] to two-and three-asset equity-linked securities (ELS). In the real finance market, two-or three-asset ELS is more popular than one-asset ELS. Therefore, we need to develop mobile platform for pricing the two-and three-asset ELS. The mobile implementation of the ELS pricing will be very useful in practice.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.26 no.4
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• pp.343-352
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• 2022

We present the user-friendly graphical user interface design and implementation of Monte Carlo simulation (MCS) for computing option price of the four-underlying asset step-down equity linked securities (ELS) using the Android platform. The ELS has been one of the most important and influential financial products in South Korea. Most ELS products are based on one-, two-, and three-underlying assets. However, currently there is a demand for higher coupon payment from ELS products because of the increased interest rate in financial market. In order to allow the investors to have higher coupon payment, it is necessary to design a multi-asset ELS such as four-asset step-down ELS. We conduct the computational experiments to demonstrate the performance of the Android platform for pricing four-asset step-down ELS. Furthermore, we perform a comparison test with a three-asset step-down ELS.