Pricing vulnerable options under jump diffusion processes using double Mellin transform

In this paper, we price the vulnerable option under the assumption that both underlying and counterparty asset price follow correlated jump diffusion processes. By the two-dimensional Itô-Doeblin formula, we initially derive a partial integro-differential equation (PIDE) satisfied by the price of th...

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Bibliographic Details
Published inCommunications in statistics. Simulation and computation Vol. 52; no. 3; pp. 703 - 716
Main Authors Li, Cuixiang, Liu, Huili, Liu, Lixia, Yao, Qiumei
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 04.03.2023
Taylor & Francis Ltd
Subjects
Differential equations
Diffusion
Double Mellin transform
Jump diffusion process
Mellin transforms
Partial integro-differential equation
Vulnerable option
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Summary:In this paper, we price the vulnerable option under the assumption that both underlying and counterparty asset price follow correlated jump diffusion processes. By the two-dimensional Itô-Doeblin formula, we initially derive a partial integro-differential equation (PIDE) satisfied by the price of the vulnerable option with flexible jumps. Then, the double Mellin transform converts the PIDE into an ordinary differential equation (ODE), which possesses an explicit solution. Further, the inverse Mellin transform of the explicit solution to the ODE turns out to be a rigorous solution to the PIDE for vulnerable option. Finally, by carrying out some numerical experiments, we demonstrate that the PIDE's solution produces price with a convincing degree of precision.
ISSN:0361-0918
1532-4141
DOI:10.1080/03610918.2020.1864645