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Analytic Method for Pricing Vulnerable External Barrier Options

Author

Listed:
  • Donghyun Kim

    (Pusan National University)

  • Ji-Hun Yoon

    (Pusan National University)

Abstract

External barrier options are financial securities that have two assets for stochastic variables, where the payoff depends on one underlying asset and the barrier depends on another state variable such that it determines whether the option is knocked in or out. In this study, considering the financial derivatives subject to the default risks of the option writer in over-the-counter markets since the global financial crisis of 2007–2008, we study vulnerable external barrier option prices by utilizing multivariate Mellin transforms and the method of images and then examine the behaviors and sensitivities of the vulnerable external barrier option prices in terms of the model parameters. Based on the results obtained, our study has two main contributions. First, by using multivariate Mellin transform approaches, we can find an explicit-form pricing formula for the option prices more effectively and easily, resolving the complexity of calculation of the option prices by using probabilistic or other methods. Second, we verify that our closed-form solution has been accurately and efficiently obtained by comparing the closed-form solution with the Monte Carlo simulation solution.

Suggested Citation

  • Donghyun Kim & Ji-Hun Yoon, 2023. "Analytic Method for Pricing Vulnerable External Barrier Options," Computational Economics, Springer;Society for Computational Economics, vol. 61(4), pages 1561-1591, April.
    • Handle: RePEc:kap:compec:v:61:y:2023:i:4:d:10.1007_s10614-022-10251-9
    DOI: 10.1007/s10614-022-10251-9
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    References listed on IDEAS

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    2. Kim, Jerim & Kim, Jeongsim & Joo Yoo, Hyun & Kim, Bara, 2015. "Pricing external barrier options in a regime-switching model," Journal of Economic Dynamics and Control, Elsevier, vol. 53(C), pages 123-143.
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