Generalizing the reflection principle of Brownian motion, and closed-form pricing of barrier options and autocallable investments

Lee, Hangsuck; Ahn, Soohan; Ko, Bangwon

doi:10.1016/j.najef.2019.101014

Cited by 12 publications

(22 citation statements)

References 11 publications

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“…In this section, we introduce a closed-form pricing of the product derived by Lee et al (2019). We first explain the product features through the most representative type in the Korean equity-linked security (ELS) market briefly.…”

Section: Framework Of Pricing Autocallable Structured Productmentioning

confidence: 99%

“…However, few studies discuss the closed-form pricing formula for ELS. Lee et al (2019) derived a closed-form pricing formula of the product using generalized reflection principle and the inclusion-exclusion principle. The formula makes it possible to compute the exact price of the investment product.…”

Section: Introductionmentioning

confidence: 99%

“…Our findings are summarized as follows: First, we rewrite the probability formula including minimum value in Lee et al (2019) in a simplified form to solve the problem of stretched out formulas caused by the inclusion-exclusion principle. Second, we transform the formulas into conditional probabilities and apply BB to compute the conditional probabilities.…”

Section: Introductionmentioning

confidence: 99%

“…The remainder of the paper is organized as follow. Section 2 summarizes the framework of pricing autocallable structured product suggested by Lee et al (2019). Section 3 introduces Brownian Bridge technique and its applicable algorithm.…”

Section: Introductionmentioning

confidence: 99%

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Semi closed-form pricing autocallable ELS using Brownian Bridge

Lee

Hong

2021

CSAM

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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.

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Section: Framework Of Pricing Autocallable Structured Productmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Semi closed-form pricing autocallable ELS using Brownian Bridge

Lee

Hong

2021

CSAM

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“…The authors illustrated the pricing of a popular auto-callable product and estimated the probability of early redemption at each auto-call date. Lee et al (2019) derived a closed-form formula that can be used for pricing step-down ELS for which the underlying asset is a single index value. Kang (2016) analyzed investment benefits of step-down ELS from the perspective of portfolio investment involving structured products.…”

Section: Introductionmentioning

confidence: 99%

A risk analysis of step-down equity-linked securities based on regime-switching copula

Nguyen

Kwon

2020

CSAM

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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.

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Multi‐step reflection principle and barrier options

Lee

Song

2022

Journal of Futures Markets

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This paper examines a class of barrier options, multi‐step barrier options, which can have any finite number of barriers of any level. We obtain a general, explicit expression for option prices of this type under the Black–Scholes model by deriving the multi‐step reflection principle, that is, the multi‐step boundary‐crossing probability of Brownian motion. Multi‐step barrier options are not only useful in that they can handle barriers of different levels and time steps but can also approximate options with arbitrary barriers. Moreover, they can be applied to pricing barrier options under jump‐diffusion models.

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Generalizing the reflection principle of Brownian motion, and closed-form pricing of barrier options and autocallable investments

Cited by 12 publications

References 11 publications

Semi closed-form pricing autocallable ELS using Brownian Bridge

Semi closed-form pricing autocallable ELS using Brownian Bridge

A risk analysis of step-down equity-linked securities based on regime-switching copula

Multi‐step reflection principle and barrier options

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