A Mellin Transform Approach to the Pricing of Options with Default Risk

Sun Yong Choi, Sotheara Veng, Jeong Hoon Kim, Ji Hun Yoon

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


The stochastic elasticity of variance model introduced by Kim et al. (Appl Stoch Models Bus Ind 30(6):753–765, 2014) is a useful model for forecasting extraordinary volatility behavior which would take place in a financial crisis and high volatility of a market could be linked to default risk of option contracts. So, it is natural to study the pricing of options with default risk under the stochastic elasticity of variance. Based on a framework with two separate scales that could minimize the number of necessary parameters for calibration but reflect the essential characteristics of the underlying asset and the firm value of the option writer, we obtain a closed form approximation formula for the option price via double Mellin transform with singular perturbation. Our formula is explicitly expressed as the Black–Scholes formula plus correction terms. The correction terms are given by the simple derivatives of the Black–Scholes solution so that the model calibration can be done very fast and effectively.

Original languageEnglish
Pages (from-to)1113-1134
Number of pages22
JournalComputational Economics
Issue number3
Publication statusPublished - 2022 Mar

Bibliographical note

Funding Information:
The work of S.-Y. Choi was supported by the National Research Foundation (NRF) of Korea (NRF-2019R1G1A1010278), The research of J.-H. Kim was supported by the NRF of Korea (NRF-2021R1A2C1004080), the research of J.-H. Yoon was supported by the NRF of Korea (NRF-2017R1A5A1015722) and (NRF-2019R1A2C108931012) and the research of S. Veng was supported by a Higher Education Improvement Project grant funded by the Cambodian Government (IDA Credit No. 6221-KH).

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

All Science Journal Classification (ASJC) codes

  • Economics, Econometrics and Finance (miscellaneous)
  • Computer Science Applications


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