Analytical pricing formulae for vulnerable vanilla and barrier options

Liang Chih Liu*, Chun Yuan Chiu, Chuan Ju Wang, Tian Shyr Dai, Hao Han Chang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
JournalReview of Quantitative Finance and Accounting
StatePublished - 29 May 2021


  • Analytical pricing formula
  • Credit risk
  • Vulnerable option


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