Analytic Method for Pricing Vulnerable External Barrier Options

Donghyun Kim () and Ji-Hun Yoon ()
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Donghyun Kim: Pusan National University
Ji-Hun Yoon: Pusan National University

Computational Economics, 2023, vol. 61, issue 4, No 9, 1591 pages

Abstract: 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.

Keywords: External barrier option; Method of images; Triple Mellin transform; Monte Carlo simulation (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10614-022-10251-9

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