• Communications for Statistical Applications and Methods
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• v.28 no.3
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• pp.251-265
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• 2021

This paper discusses the pricing of autocallable structured product with knock-in (KI) feature using the exit probability with the Brownian Bridge technique. The explicit pricing formula of autocallable ELS derived in the existing paper handles the part including the minimum of the Brownian motion using the inclusion-exclusion principle. This has the disadvantage that the pricing formula is complicate because of the probability with minimum value and the computational volume increases dramatically as the number of autocall chances increases. To solve this problem, we applied an efficient and robust simulation method called the Brownian Bridge technique, which provides the probability of touching the predetermined barrier when the initial and terminal values of the process following the Brownian motion in a certain interval are specified. We rewrite the existing pricing formula and provide a brief theoretical background and computational algorithm for the technique. We also provide several numerical examples computed in three different ways: explicit pricing formula, the Crude Monte Carlo simulation method and the Brownian Bridge technique.

• 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.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.