News Release

The price is right: Pusan National University scientists develop new model to determine pricing of vulnerable exchange options

The new model makes use of ‘double Mellin transforms’ and the ‘method of dimension reduction’ to provide an effective and accurate mathematical solution

Peer-Reviewed Publication

Pusan National University

Researchers suggest an explicit-closed form solution for the pricing of vulnerable exchange options with early counterparty credit risk, providing an accurate and efficient solution for portfolio allocation

image: An infographic depicting the advantages of the new model for the pricing of vulnerable exchange options view more 

Credit: Pusan National University

The global financial crisis in 2007–08 devastated markets worldwide and created a sea change in how we conduct finance. The over-the-counter (OTC) market has flourished in the aftermath of the global financial crisis. In an OTC, two parties can directly trade stocks, commodities etc. with each other and without the use of a central exchange or broker. This has, however, made the option holder permanently open to default risk. Modeling the prices of these options in the OTC market is complicated, with most existing models falling short. In a new study, published in North American Journal of Economics and Finance, researchers suggest a way to effectively and accurately price vulnerable options while accounting for the risk of the counterparty defaulting on their commitment, i.e., counterparty credit risk. “The exchange option enables its option holder, who holds two underlying assets, to exchange one asset for the other. But when does one apply this strategy? That is what we have aimed to answer in our work,” says Prof. Ji-Hun Yoon, Associate Professor at Pusan National University, who led the study.

The exchange option offers a means by which an investor can improve the performance of risk adjustment, as well as mitigate the risk of drastic portfolio depreciation. This is crucial when an investor holds risky assets. The exchange option allows the investor to offset the risk and allows them to aim towards more stability and profitability.

For their model, the research team used three key mathematical techniques—the ‘method of dimension reduction,’ ‘double Mellin transforms,’ and the ‘method of images.’ By applying these complicated techniques, they were able to derive an explicit-closed form solution to the problem of vulnerable exchange option pricing. The primary advantage of an explicit solution lies in the efficacy of its final calculations, enabling its quick deployment without the need to wait for long calculations on a computer. The research team then compared their model to the standard vulnerable exchange option (VEO) model and found their results to be sufficiently similar. Finally, they confirmed the accuracy of their result by checking it against the formula derived using ‘Monte-Carlo simulation,’ which is a computationally intense but accurate method.

“Pricing the model dynamics of financial derivatives in a way that reflects the current situation in the OTC market is very important,” explains Prof. Yoon. “Our work can be applied to the pricing of diverse financial derivatives and enable effective portfolio allocation.”

These findings are sure to have a significant effect on how people choose to invest and manage their portfolios in the future.




Authors: Donghyun Kim1, Geonwoo Kim2, Ji-HunYoon1


  1. Department of Mathematics, Pusan National University, Republic of Korea
  2. The School of Liberal Arts, Seoul National University of Science and Technology, Republic of Korea


About Pusan National University
Pusan National University, located in Busan, South Korea, was founded in 1946, and is now the no. 1 national university of South Korea in research and educational competency. The multi-campus university also has other smaller campuses in Yangsan, Miryang, and Ami. The university prides itself on the principles of truth, freedom, and service, and has approximately 30,000 students, 1200 professors, and 750 faculty members. The university is composed of 14 colleges (schools) and one independent division, with 103 departments in all.    


About the author
Professor Ji-Hun Yoon is an Associate Professor at the Department of Mathematics in Pusan National University. Dr. Yoon’s group researches the derivation of closed-form solutions for the diverse financial derivatives or options calibration, by using the options data from the financial market. In 2013, he received his PhD degree from Yonsei University, and later worked as a postdoctoral fellow at Seoul National University. In 2015, he was appointed as Assistant Professor at the Department of Mathematics in Pusan National University. He has several research articles published in reputed journals, to his credit.

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