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Pricing two-asset alternating barrier options with icicles and their variations

Authors
Lee, HangsuckKim, EunchaeSong, Seongjoo
Issue Date
6월-2020
Publisher
SPRINGER HEIDELBERG
Keywords
Alternating barrier option; Icicled barrier option; Equity-linked products; Brownian motion; Esscher transform; Factorization formula
Citation
JOURNAL OF THE KOREAN STATISTICAL SOCIETY, v.49, no.2, pp.626 - 672
Indexed
SCIE
SCOPUS
KCI
Journal Title
JOURNAL OF THE KOREAN STATISTICAL SOCIETY
Volume
49
Number
2
Start Page
626
End Page
672
URI
https://scholar.korea.ac.kr/handle/2021.sw.korea/55441
DOI
10.1007/s42952-019-00039-3
ISSN
1226-3192
Abstract
This paper introduces a new class of barrier options and its variations. We call the new class of options as two-asset alternating barrier options, since we consider alternating barrier levels for two underlying assets. The alternating barrier levels are placed in the sub-periods of the option's lifetime; each being applied to one of the two underlying assets. We also consider vertical branches of the barrier, which are termed as icicles. The alternating barrier with icicles can be often seen as an embedded form in various equity-linked financial products. To price such new options, we obtain the joint distribution of two underlying asset prices at an intermediate time point and the maturity, along with their partial maximums under the Black-Scholes model. This joint distribution plays a critical role in the derivation of the pricing formulas for alternating barrier options and their variants. As in ordinary barrier options, we consider eight types of alternating barrier options and derive their explicit option pricing formulas. To our knowledge, the pricing formulas for these options have never been obtained explicitly in the literature even under the Black-Scholes model. We also examine an autocallable equity-linked investment product to derive its explicit pricing formula. Our results are illustrated with numerical examples, showing the effect of different barrier levels and different values of correlation coefficient between two underlying asset prices.
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Song, Seongjoo
정경대학 (통계학과)
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