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Review of Quantitative Finance and Accounting

Erschienen in:

29.05.2021 | Original Research

Analytical pricing formulae for vulnerable vanilla and barrier options

verfasst von: Liang-Chih Liu, Chun-Yuan Chiu, Chuan-Ju Wang, Tian-Shyr Dai, Hao-Han Chang

Erschienen in: Review of Quantitative Finance and Accounting | Ausgabe 1/2022

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Abstract

This paper proposes analytically vulnerable vanilla option pricing formulae that simultaneously consider the premature default, the correlation between the underlying asset and the issuer’s asset, and other outstanding debts of the issuer. Our pricing formulae can be easily extended to solve the problem of pricing vulnerable barrier options, which has been rarely studied before. We show that previous studies on pricing (non)-vulnerable vanilla options and barrier options are degenerate cases of our formulae. We conduct numerical experiments to analyze the relations among the financial/contract parameters and counterparty risk, and also empirically evaluate vulnerable vanilla warrants on the TAIEX issued by Capital Securities with detailed studies of parameter calibrations to examine the robustness of our approach.

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TAIEX is the abbreviation for Taiwan Capitalization Weighted Stock Index, a stock market index for companies traded on the Taipei Stock Exchange.

We thank a referee for reminding us of this contract feature.

This assumption is mild since derivatives usually play tiny roles in many firms’ debt obligations as in Klein (1996).

Note that \(\lim _{x\rightarrow \infty }N_2(x, y, \rho ) = N_1(y)\) for any arbitrary constants \(\rho \) and y.

Note that the pricing formula for vulnerable vanilla calls in Klein (1996) is derived under Merton’s model, whereas the formula in Sec. 3 of this paper is derived under the first-passage model.

Note that \(\lim _{x\rightarrow \infty }N_2(x, y, \rho ) = N_1(y)\) for any arbitrary constants \(\rho \) and y.

These two parameters are not required for pricing vulnerable vanilla options.

See http://www.taifex.com.tw/cht/3/optDailyMarketReport.

See https://www.ba.org.tw/Taibor/TaiborList?type=DayHistory.

Note that TAIEX options can still be treated as the otherwise almost identical non-vulnerable counterparts of our target warrants, due to a small average interval \(\tau = 30\) min.

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Titel: Analytical pricing formulae for vulnerable vanilla and barrier options
verfasst von: Liang-Chih Liu
Chun-Yuan Chiu
Chuan-Ju Wang
Tian-Shyr Dai
Hao-Han Chang
Publikationsdatum: 29.05.2021
Verlag: Springer US
Erschienen in: Review of Quantitative Finance and Accounting / Ausgabe 1/2022
Print ISSN: 0924-865X
Elektronische ISSN: 1573-7179
DOI: https://doi.org/10.1007/s11156-021-00990-5

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